Become a Linear Algebra Master
About Course
Learn linear algebra for free with this comprehensive course from Udemy. Master the fundamentals of linear algebra with 247 lessons, 69 quizzes, and 12 workbooks. This course is designed to make complicated math easy. You’ll learn about operations on matrices, dot and cross products, transformations, inverses, determinants, orthogonality, change of basis, eigenvalues, and eigenvectors.
This free linear algebra course covers:
 Operations on one matrix, including solving linear systems and GaussJordan elimination
 Operations on two matrices, including matrix multiplication and elimination matrices
 Matrices as vectors, including linear combinations and span, linear independence, and subspaces
 Dot products and cross products, including the CauchySchwarz and vector triangle inequalities
 Matrixvector products, including the null and column spaces, and solving Ax=b
 Transformations, including linear transformations, projections, and composition of transformations
 Inverses, including invertible and singular matrices, and solving systems with inverse matrices
 Determinants, including upper and lower triangular matrices, and Cramer’s rule
 Transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose
 Orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis
 Orthonormal bases and GramSchmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the GramSchmidt process
 Eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions
This free course includes video explanations, notes, quizzes, and workbooks with practice problems.
This course is from Udemy, Udacity, Coursera, MasterClass, NearPeer, and other platforms. Start learning linear algebra today!
What Will You Learn?
 Operations on one matrix, including solving linear systems, and GaussJordan elimination
 Operations on two matrices, including matrix multiplication and elimination matrices
 Matrices as vectors, including linear combinations and span, linear independence, and subspaces
 Dot products and cross products, including the CauchySchwarz and vector triangle inequalities
 Matrixvector products, including the null and column spaces, and solving Ax=b
 Transformations, including linear transformations, projections, and composition of transformations
 Inverses, including invertible and singular matrices, and solving systems with inverse matrices
 Determinants, including upper and lower triangular matrices, and Cramer's rule
 Transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose
 Orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis
 Orthonormal bases and GramSchmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the GramSchmidt process
 Eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions
Course Content
01 – Getting started

A Message from the Professor

001 What we’ll learn in this course.mp4
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002 How to get the most out of this course.mp4
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003 Download the formula sheet.html
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004 The EVERYTHING download.html
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Section Quiz
02 – Operations on one matrix

001 Introduction to operations on one matrix.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Linear systems in two unknowns.html
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004 Linear systems in two unknowns.mp4
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005 Linear systems in two unknowns.html
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006 Linear systems in three unknowns.html
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007 Linear systems in three unknowns.mp4
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008 Linear systems in three unknowns.html
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009 Matrix dimensions and entries.html
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010 Matrix dimensions and entries.mp4
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011 Matrix dimensions and entries.html
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012 Representing systems with matrices.html
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013 Representing systems with matrices.mp4
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014 Representing systems with matrices.html
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015 Simple row operations.html
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016 Simple row operations.mp4
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017 Simple row operations.html
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018 Pivot entries and rowechelon forms.html
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019 Pivot entries and rowechelon forms.mp4
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020 Pivot entries and rowechelon forms.html
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021 GaussJordan elimination.html
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022 GaussJordan elimination.mp4
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023 GaussJordan elimination.html
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024 Number of solutions to the linear system.html
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025 Number of solutions to the linear system.mp4
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026 Number of solutions to the linear system.html
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027 BONUS! Extra practice problems. ).html
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Section Quiz
03 – Operations on two matrices

001 Introduction to operations on two matrices.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Matrix addition and subtraction.html
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004 Matrix addition and subtraction.mp4
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005 Matrix addition and subtraction.html
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006 Scalar multiplication.html
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007 Scalar multiplication.mp4
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008 Scalar multiplication.html
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009 Zero matrices.html
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010 Zero matrices.mp4
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011 Zero matrices.html
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012 Matrix multiplication.html
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013 Matrix multiplication.mp4
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014 Matrix multiplication.html
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015 Identity matrices.html
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016 Identity matrices.mp4
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017 Identity matrices.html
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018 The elimination matrix.html
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019 The elimination matrix.mp4
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020 The elimination matrix.html
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021 BONUS! Extra practice problems. ).html
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Section Quiz
04 – Matrices as vectors

001 Introduction to matrices as vectors.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Vectors.html
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004 Vectors.mp4
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005 Vectors.html
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006 Vector operations.html
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007 Vector operations.mp4
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008 Vector operations.html
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009 Unit vectors and basis vectors.html
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010 Unit vectors and basis vectors.mp4
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011 Unit vectors and basis vectors.html
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012 Linear combinations and span.html
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013 Linear combinations and span.mp4
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014 Linear combinations and span.html
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015 Linear independence in two dimensions.html
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016 Linear independence in two dimensions.mp4
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017 Linear independence in two dimensions.html
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018 Linear independence in three dimensions.html
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019 Linear independence in three dimensions.mp4
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020 Linear independence in three dimensions.html
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021 Linear subspaces.html
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022 Linear subspaces.mp4
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023 Linear subspaces.html
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024 Spans as subspaces.html
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025 Spans as subspaces.mp4
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026 Spans as subspaces.html
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027 Basis.html
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028 Basis.mp4
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029 Basis.html
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030 BONUS! Extra practice problems. ).html
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Section Quiz
05 – Dot products and cross products

001 Introduction to dot products and cross products.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Dot products.html
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004 Dot products.mp4
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005 Dot products.html
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006 CauchySchwarz inequality.html
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007 CauchySchwarz inequality.mp4
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008 CauchySchwarz inequality.html
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009 Vector triangle inequality.html
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010 Vector triangle inequality.mp4
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011 Vector triangle inequality.html
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012 Angle between vectors.html
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013 Angle between vectors.mp4
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014 Angle between vectors.html
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015 Equation of a plane, and normal vectors.html
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016 Equation of a plane, and normal vectors.mp4
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017 Equation of a plane, and normal vectors.html
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018 Cross products.html
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019 Cross products.mp4
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020 Cross products.html
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021 Dot and cross products as opposite ideas.html
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022 Dot and cross products as opposite ideas.mp4
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023 Dot and cross products as opposite ideas.html
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024 BONUS! Extra practice problems. ).html
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Section Quiz
06 – Matrixvector products

001 Introduction to matrixvector products.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Multiplying matrices by vectors.html
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004 Multiplying matrices by vectors.mp4
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005 Multiplying matrices by vectors.html
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006 The null space and Ax=O.html
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007 The null space and Ax=O.mp4
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008 The null space and Ax=O.html
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009 Null space of a matrix.html
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010 Null space of a matrix.mp4
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011 Null space of a matrix.html
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012 The column space and Ax=b.html
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013 The column space and Ax=b.mp4
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014 The column space and Ax=b.html
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015 Solving Ax=b.html
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016 Solving Ax=b.mp4
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017 Solving Ax=b.html
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018 Dimensionality, nullity, and rank.html
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019 Dimensionality, nullity, and rank.mp4
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020 Dimensionality, nullity, and rank.html
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021 BONUS! Extra practice problems. ).html
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Section Quiz
07 – Transformations

001 Introduction to transformations.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Functions and transformations.html
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004 Functions and transformations.mp4
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005 Functions and transformations.html
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006 Transformation matrices and the image of the subset.html
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007 Transformation matrices and the image of the subset.mp4
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008 Transformation matrices and the image of the subset.html
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009 Preimage, image, and the kernel.html
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010 Preimage, image, and the kernel.mp4
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011 Preimage, image, and the kernel.html
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012 Linear transformations as matrixvector products.html
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013 Linear transformations as matrixvector products.mp4
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014 Linear transformations as matrixvector products.html
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015 Linear transformations as rotations.html
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016 Linear transformations as rotations.mp4
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017 Linear transformations as rotations.html
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018 Adding and scaling linear transformations.html
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019 Adding and scaling linear transformations.mp4
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020 Adding and scaling linear transformations.html
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021 Projections as linear transformations.html
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022 Projections as linear transformations.mp4
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023 Projections as linear transformations.html
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024 Compositions of linear transformations.html
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025 Compositions of linear transformations.mp4
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026 Compositions of linear transformations.html
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027 BONUS! Extra practice problems. ).html
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Section Quiz
08 – Inverses

001 Introduction to inverses.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Inverse of a transformation.html
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004 Inverse of a transformation.mp4
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005 Inverse of a transformation.html
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006 Invertibility from the matrixvector product.html
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007 Invertibility from the matrixvector product.mp4
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008 Invertibility from the matrixvector product.html
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009 Inverse transformations are linear.html
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010 Inverse transformations are linear.mp4
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011 Inverse transformations are linear.html
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012 Matrix inverses, and invertible and singular matrices.html
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013 Matrix inverses, and invertible and singular matrices.mp4
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014 Matrix inverses, and invertible and singular matrices.html
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015 Solving systems with inverse matrices.html
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016 Solving systems with inverse matrices.mp4
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017 Solving systems with inverse matrices.html
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018 BONUS! Extra practice problems. ).html
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Section Quiz
09 – Determinants

001 Introduction to determinants.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Determinants.html
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004 Determinants.mp4
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005 Determinants.html
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006 Cramer’s rule for solving systems.html
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007 Cramer’s rule for solving systems.mp4
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008 Cramer’s rule for solving systems.html
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009 Modifying determinants.html
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010 Modifying determinants.mp4
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011 Modifying determinants.html
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012 Upper and lower triangular matrices.html
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013 Upper and lower triangular matrices.mp4
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014 Upper and lower triangular matrices.html
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015 Using determinants to find area.html
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016 Using determinants to find area.mp4
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017 Using determinants to find area.html
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018 BONUS! Extra practice problems. ).html
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Section Quiz
10 – Transposes

001 Introduction to transposes.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Transposes and their determinants.html
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004 Transposes and their determinants.mp4
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005 Transposes and their determinants.html
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006 Transposes of products, sums, and inverses.html
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007 Transposes of products, sums, and inverses.mp4
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008 Transposes of products, sums, and inverses.html
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009 Null and column spaces of the transpose.html
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010 Null and column spaces of the transpose.mp4
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011 Null and column spaces of the transpose.html
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012 The product of a matrix and its transpose.html
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013 The product of a matrix and its transpose.mp4
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014 The product of a matrix and its transpose.html
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015 BONUS! Extra practice problems. ).html
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Section Quiz
11 – Orthogonality and change of basis

001 Introduction to orthogonality and change of basis.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Orthogonal complements.html
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004 Orthogonal complements.mp4
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005 Orthogonal complements.html
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006 Orthogonal complements of the fundamental subspaces.html
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007 Orthogonal complements of the fundamental subspaces.mp4
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008 Orthogonal complements of the fundamental subspaces.html
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009 Projection onto the subspace.html
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010 Projection onto the subspace.mp4
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011 Projection onto the subspace.html
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012 Least squares solution.html
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013 Least squares solution.mp4
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014 Least squares solution.html
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015 Coordinates in a new basis.html
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016 Coordinates in a new basis.mp4
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017 Coordinates in a new basis.html
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018 Transformation matrix for a basis.html
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019 Transformation matrix for a basis.mp4
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020 Transformation matrix for a basis.html
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021 BONUS! Extra practice problems. ).html
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Section Quiz
12 – Orthonormal bases and GramSchmidt

001 Introduction to orthonormal bases and GramSchmidt.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Orthonormal bases.html
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004 Orthonormal bases.mp4
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005 Orthonormal bases.html
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006 Projection onto an orthonormal basis.html
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007 Projection onto an orthonormal basis.mp4
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008 Projection onto an orthonormal basis.html
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009 GramSchmidt process for change of basis.html
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010 GramSchmidt process for change of basis.mp4
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011 GramSchmidt process for change of basis.html
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012 BONUS! Extra practice problems. ).html
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Section Quiz
13 – Eigenvalues and Eigenvectors

001 Introduction to Eigenvalues and Eigenvectors.mp4
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002 RESOURCE Quiz solutions for this section.html
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003 Eigenvalues, eigenvectors, eigenspaces.html
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004 Eigenvalues, eigenvectors, eigenspaces.mp4
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005 Eigenvalues, eigenvectors, eigenspaces.html
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006 Eigen in three dimensions.html
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007 Eigen in three dimensions.mp4
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008 Eigen in three dimensions.html
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009 BONUS! Extra practice problems. ).html
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Section Quiz
14 – Final exam and wrapup

001 Practice final exam #1 (optional).html
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002 Practice final exam #2 (optional).html
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003 Linear Algebra final exam.html
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004 Wrapup.mp4
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