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 Gauss-Jordan 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 Cauchy-Schwarz and vector triangle inequalities
Matrix-vector 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 Gram-Schmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt 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!

Operations on one matrix, including solving linear systems, and Gauss-Jordan 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 Cauchy-Schwarz and vector triangle inequalities
Matrix-vector 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 Gram-Schmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt 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

00:00
002 How to get the most out of this course.mp4

00:00
003 Download the formula sheet.html

00:00
004 The EVERYTHING download.html

00:00
Section Quiz

02 – Operations on one matrix

001 Introduction to operations on one matrix.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Linear systems in two unknowns.html

00:00
004 Linear systems in two unknowns.mp4

00:00
005 Linear systems in two unknowns.html

00:00
006 Linear systems in three unknowns.html

00:00
007 Linear systems in three unknowns.mp4

00:00
008 Linear systems in three unknowns.html

00:00
009 Matrix dimensions and entries.html

00:00
010 Matrix dimensions and entries.mp4

00:00
011 Matrix dimensions and entries.html

00:00
012 Representing systems with matrices.html

00:00
013 Representing systems with matrices.mp4

00:00
014 Representing systems with matrices.html

00:00
015 Simple row operations.html

00:00
016 Simple row operations.mp4

00:00
017 Simple row operations.html

00:00
018 Pivot entries and row-echelon forms.html

00:00
019 Pivot entries and row-echelon forms.mp4

00:00
020 Pivot entries and row-echelon forms.html

00:00
021 Gauss-Jordan elimination.html

00:00
022 Gauss-Jordan elimination.mp4

00:00
023 Gauss-Jordan elimination.html

00:00
024 Number of solutions to the linear system.html

00:00
025 Number of solutions to the linear system.mp4

00:00
026 Number of solutions to the linear system.html

00:00
027 BONUS! Extra practice problems. ).html

00:00
Section Quiz

03 – Operations on two matrices

001 Introduction to operations on two matrices.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Matrix addition and subtraction.html

00:00
004 Matrix addition and subtraction.mp4

00:00
005 Matrix addition and subtraction.html

00:00
006 Scalar multiplication.html

00:00
007 Scalar multiplication.mp4

00:00
008 Scalar multiplication.html

00:00
009 Zero matrices.html

00:00
010 Zero matrices.mp4

00:00
011 Zero matrices.html

00:00
012 Matrix multiplication.html

00:00
013 Matrix multiplication.mp4

00:00
014 Matrix multiplication.html

00:00
015 Identity matrices.html

00:00
016 Identity matrices.mp4

00:00
017 Identity matrices.html

00:00
018 The elimination matrix.html

00:00
019 The elimination matrix.mp4

00:00
020 The elimination matrix.html

00:00
021 BONUS! Extra practice problems. ).html

00:00
Section Quiz

04 – Matrices as vectors

001 Introduction to matrices as vectors.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Vectors.html

00:00
004 Vectors.mp4

00:00
005 Vectors.html

00:00
006 Vector operations.html

00:00
007 Vector operations.mp4

00:00
008 Vector operations.html

00:00
009 Unit vectors and basis vectors.html

00:00
010 Unit vectors and basis vectors.mp4

00:00
011 Unit vectors and basis vectors.html

00:00
012 Linear combinations and span.html

00:00
013 Linear combinations and span.mp4

00:00
014 Linear combinations and span.html

00:00
015 Linear independence in two dimensions.html

00:00
016 Linear independence in two dimensions.mp4

00:00
017 Linear independence in two dimensions.html

00:00
018 Linear independence in three dimensions.html

00:00
019 Linear independence in three dimensions.mp4

00:00
020 Linear independence in three dimensions.html

00:00
021 Linear subspaces.html

00:00
022 Linear subspaces.mp4

00:00
023 Linear subspaces.html

00:00
024 Spans as subspaces.html

00:00
025 Spans as subspaces.mp4

00:00
026 Spans as subspaces.html

00:00
027 Basis.html

00:00
028 Basis.mp4

00:00
029 Basis.html

00:00
030 BONUS! Extra practice problems. ).html

00:00
Section Quiz

05 – Dot products and cross products

001 Introduction to dot products and cross products.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Dot products.html

00:00
004 Dot products.mp4

00:00
005 Dot products.html

00:00
006 Cauchy-Schwarz inequality.html

00:00
007 Cauchy-Schwarz inequality.mp4

00:00
008 Cauchy-Schwarz inequality.html

00:00
009 Vector triangle inequality.html

00:00
010 Vector triangle inequality.mp4

00:00
011 Vector triangle inequality.html

00:00
012 Angle between vectors.html

00:00
013 Angle between vectors.mp4

00:00
014 Angle between vectors.html

00:00
015 Equation of a plane, and normal vectors.html

00:00
016 Equation of a plane, and normal vectors.mp4

00:00
017 Equation of a plane, and normal vectors.html

00:00
018 Cross products.html

00:00
019 Cross products.mp4

00:00
020 Cross products.html

00:00
021 Dot and cross products as opposite ideas.html

00:00
022 Dot and cross products as opposite ideas.mp4

00:00
023 Dot and cross products as opposite ideas.html

00:00
024 BONUS! Extra practice problems. ).html

00:00
Section Quiz

06 – Matrix-vector products

001 Introduction to matrix-vector products.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Multiplying matrices by vectors.html

00:00
004 Multiplying matrices by vectors.mp4

00:00
005 Multiplying matrices by vectors.html

00:00
006 The null space and Ax=O.html

00:00
007 The null space and Ax=O.mp4

00:00
008 The null space and Ax=O.html

00:00
009 Null space of a matrix.html

00:00
010 Null space of a matrix.mp4

00:00
011 Null space of a matrix.html

00:00
012 The column space and Ax=b.html

00:00
013 The column space and Ax=b.mp4

00:00
014 The column space and Ax=b.html

00:00
015 Solving Ax=b.html

00:00
016 Solving Ax=b.mp4

00:00
017 Solving Ax=b.html

00:00
018 Dimensionality, nullity, and rank.html

00:00
019 Dimensionality, nullity, and rank.mp4

00:00
020 Dimensionality, nullity, and rank.html

00:00
021 BONUS! Extra practice problems. ).html

00:00
Section Quiz

07 – Transformations

001 Introduction to transformations.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Functions and transformations.html

00:00
004 Functions and transformations.mp4

00:00
005 Functions and transformations.html

00:00
006 Transformation matrices and the image of the subset.html

00:00
007 Transformation matrices and the image of the subset.mp4

00:00
008 Transformation matrices and the image of the subset.html

00:00
009 Preimage, image, and the kernel.html

00:00
010 Preimage, image, and the kernel.mp4

00:00
011 Preimage, image, and the kernel.html

00:00
012 Linear transformations as matrix-vector products.html

00:00
013 Linear transformations as matrix-vector products.mp4

00:00
014 Linear transformations as matrix-vector products.html

00:00
015 Linear transformations as rotations.html

00:00
016 Linear transformations as rotations.mp4

00:00
017 Linear transformations as rotations.html

00:00
018 Adding and scaling linear transformations.html

00:00
019 Adding and scaling linear transformations.mp4

00:00
020 Adding and scaling linear transformations.html

00:00
021 Projections as linear transformations.html

00:00
022 Projections as linear transformations.mp4

00:00
023 Projections as linear transformations.html

00:00
024 Compositions of linear transformations.html

00:00
025 Compositions of linear transformations.mp4

00:00
026 Compositions of linear transformations.html

00:00
027 BONUS! Extra practice problems. ).html

00:00
Section Quiz

08 – Inverses

001 Introduction to inverses.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Inverse of a transformation.html

00:00
004 Inverse of a transformation.mp4

00:00
005 Inverse of a transformation.html

00:00
006 Invertibility from the matrix-vector product.html

00:00
007 Invertibility from the matrix-vector product.mp4

00:00
008 Invertibility from the matrix-vector product.html

00:00
009 Inverse transformations are linear.html

00:00
010 Inverse transformations are linear.mp4

00:00
011 Inverse transformations are linear.html

00:00
012 Matrix inverses, and invertible and singular matrices.html

00:00
013 Matrix inverses, and invertible and singular matrices.mp4

00:00
014 Matrix inverses, and invertible and singular matrices.html

00:00
015 Solving systems with inverse matrices.html

00:00
016 Solving systems with inverse matrices.mp4

00:00
017 Solving systems with inverse matrices.html

00:00
018 BONUS! Extra practice problems. ).html

00:00
Section Quiz

09 – Determinants

001 Introduction to determinants.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Determinants.html

00:00
004 Determinants.mp4

00:00
005 Determinants.html

00:00
006 Cramer’s rule for solving systems.html

00:00
007 Cramer’s rule for solving systems.mp4

00:00
008 Cramer’s rule for solving systems.html

00:00
009 Modifying determinants.html

00:00
010 Modifying determinants.mp4

00:00
011 Modifying determinants.html

00:00
012 Upper and lower triangular matrices.html

00:00
013 Upper and lower triangular matrices.mp4

00:00
014 Upper and lower triangular matrices.html

00:00
015 Using determinants to find area.html

00:00
016 Using determinants to find area.mp4

00:00
017 Using determinants to find area.html

00:00
018 BONUS! Extra practice problems. ).html

00:00
Section Quiz

10 – Transposes

001 Introduction to transposes.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Transposes and their determinants.html

00:00
004 Transposes and their determinants.mp4

00:00
005 Transposes and their determinants.html

00:00
006 Transposes of products, sums, and inverses.html

00:00
007 Transposes of products, sums, and inverses.mp4

00:00
008 Transposes of products, sums, and inverses.html

00:00
009 Null and column spaces of the transpose.html

00:00
010 Null and column spaces of the transpose.mp4

00:00
011 Null and column spaces of the transpose.html

00:00
012 The product of a matrix and its transpose.html

00:00
013 The product of a matrix and its transpose.mp4

00:00
014 The product of a matrix and its transpose.html

00:00
015 BONUS! Extra practice problems. ).html

00:00
Section Quiz

11 – Orthogonality and change of basis

001 Introduction to orthogonality and change of basis.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Orthogonal complements.html

00:00
004 Orthogonal complements.mp4

00:00
005 Orthogonal complements.html

00:00
006 Orthogonal complements of the fundamental subspaces.html

00:00
007 Orthogonal complements of the fundamental subspaces.mp4

00:00
008 Orthogonal complements of the fundamental subspaces.html

00:00
009 Projection onto the subspace.html

00:00
010 Projection onto the subspace.mp4

00:00
011 Projection onto the subspace.html

00:00
012 Least squares solution.html

00:00
013 Least squares solution.mp4

00:00
014 Least squares solution.html

00:00
015 Coordinates in a new basis.html

00:00
016 Coordinates in a new basis.mp4

00:00
017 Coordinates in a new basis.html

00:00
018 Transformation matrix for a basis.html

00:00
019 Transformation matrix for a basis.mp4

00:00
020 Transformation matrix for a basis.html

00:00
021 BONUS! Extra practice problems. ).html

00:00
Section Quiz

12 – Orthonormal bases and Gram-Schmidt

001 Introduction to orthonormal bases and Gram-Schmidt.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Orthonormal bases.html

00:00
004 Orthonormal bases.mp4

00:00
005 Orthonormal bases.html

00:00
006 Projection onto an orthonormal basis.html

00:00
007 Projection onto an orthonormal basis.mp4

00:00
008 Projection onto an orthonormal basis.html

00:00
009 Gram-Schmidt process for change of basis.html

00:00
010 Gram-Schmidt process for change of basis.mp4

00:00
011 Gram-Schmidt process for change of basis.html

00:00
012 BONUS! Extra practice problems. ).html

00:00
Section Quiz

13 – Eigenvalues and Eigenvectors

001 Introduction to Eigenvalues and Eigenvectors.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Eigenvalues, eigenvectors, eigenspaces.html

00:00
004 Eigenvalues, eigenvectors, eigenspaces.mp4

00:00
005 Eigenvalues, eigenvectors, eigenspaces.html

00:00
006 Eigen in three dimensions.html

00:00
007 Eigen in three dimensions.mp4

00:00
008 Eigen in three dimensions.html

00:00
009 BONUS! Extra practice problems. ).html

00:00
Section Quiz

14 – Final exam and wrap-up

Add this certificate to your resume to demonstrate your skills & increase your chances of getting noticed.

Student Ratings & Reviews

No Review Yet

About Course

What Will You Learn?

Course Content

01 – Getting started

A Message from the Professor

001 What we’ll learn in this course.mp4

002 How to get the most out of this course.mp4

003 Download the formula sheet.html

004 The EVERYTHING download.html

Section Quiz

02 – Operations on one matrix

001 Introduction to operations on one matrix.mp4

002 RESOURCE Quiz solutions for this section.html

003 Linear systems in two unknowns.html

004 Linear systems in two unknowns.mp4

005 Linear systems in two unknowns.html

006 Linear systems in three unknowns.html

007 Linear systems in three unknowns.mp4

008 Linear systems in three unknowns.html

009 Matrix dimensions and entries.html

010 Matrix dimensions and entries.mp4

011 Matrix dimensions and entries.html

012 Representing systems with matrices.html

013 Representing systems with matrices.mp4

014 Representing systems with matrices.html

015 Simple row operations.html

016 Simple row operations.mp4

017 Simple row operations.html

018 Pivot entries and row-echelon forms.html

019 Pivot entries and row-echelon forms.mp4

020 Pivot entries and row-echelon forms.html

021 Gauss-Jordan elimination.html

022 Gauss-Jordan elimination.mp4

023 Gauss-Jordan elimination.html

024 Number of solutions to the linear system.html

025 Number of solutions to the linear system.mp4

026 Number of solutions to the linear system.html

027 BONUS! Extra practice problems. ).html

Section Quiz

03 – Operations on two matrices

001 Introduction to operations on two matrices.mp4

002 RESOURCE Quiz solutions for this section.html

003 Matrix addition and subtraction.html

004 Matrix addition and subtraction.mp4

005 Matrix addition and subtraction.html

006 Scalar multiplication.html

007 Scalar multiplication.mp4

008 Scalar multiplication.html

009 Zero matrices.html

010 Zero matrices.mp4

011 Zero matrices.html

012 Matrix multiplication.html

013 Matrix multiplication.mp4

014 Matrix multiplication.html

015 Identity matrices.html

016 Identity matrices.mp4

017 Identity matrices.html

018 The elimination matrix.html

019 The elimination matrix.mp4

020 The elimination matrix.html

021 BONUS! Extra practice problems. ).html

Section Quiz

04 – Matrices as vectors

001 Introduction to matrices as vectors.mp4

002 RESOURCE Quiz solutions for this section.html

003 Vectors.html

004 Vectors.mp4

005 Vectors.html

006 Vector operations.html

007 Vector operations.mp4

008 Vector operations.html

009 Unit vectors and basis vectors.html

010 Unit vectors and basis vectors.mp4

011 Unit vectors and basis vectors.html

012 Linear combinations and span.html

013 Linear combinations and span.mp4

014 Linear combinations and span.html

015 Linear independence in two dimensions.html

016 Linear independence in two dimensions.mp4

017 Linear independence in two dimensions.html