Linear Algebra

This course is based on: Linear Algebra and Its Applications (5th Edition)
Last Updated: April 29, 2020


Linear Algebra is the branch of mathematics that provides a framework to operate on matrices, which allow for more efficient computations in various applications in Computer Graphics, Machine Learning, Linear Programming, etc.


Recommended Prerequisites: None

Chapter 1
Chapter 1.1: Systems of Linear Equations
Linear Algebra Part 4 (System of Linear equations) || Engineering Mathematics for GATE Views: 170K; Net Likes: 1.63K; Like Ratio: 97%; Length: 58m
Introduction to Linear Algebra: Systems of Linear Equations Views: 26.8K; Net Likes: 505; Like Ratio: 99%; Length: 10m
Introduction to Systems of Linear Equations (TTP Video 47) Views: 31.8K; Net Likes: 410; Like Ratio: 97%; Length: 17m
Linear Algebra Example Problems - General Solution of Augmented Matrix Views: 60.2K; Net Likes: 359; Like Ratio: 96%; Length: 8m
Chapter 1.2: Row Reduction and Echelon Forms
Row Reducing a Matrix - Systems of Linear Equations - Part 1 Views: 594K; Net Likes: 2.32K; Like Ratio: 95%; Length: 10m
Gauss Jordan Elimination & Reduced Row Echelon Form Views: 233K; Net Likes: 2.16K; Like Ratio: 95%; Length: 10m
Elementary Linear Algebra: Echelon Form of a Matrix, Part 1 Views: 162K; Net Likes: 1.68K; Like Ratio: 97%; Length: 5m
Reduced Row Echelon Form - #1 Skill in Linear Algebra Views: 81.4K; Net Likes: 1.37K; Like Ratio: 98%; Length: 50m
Chapter 1.3: Vector Equations
Parametric representations of lines | Vectors and spaces | Linear Algebra | Khan Academy Views: 628K; Net Likes: 1.08K; Like Ratio: 96%; Length: 24m
Vector intro for linear algebra | Vectors and spaces | Linear Algebra | Khan Academy Views: 975K; Net Likes: 857; Like Ratio: 98%; Length: 5m
Linear Algebra: Introduction to Vectors Views: 417K; Net Likes: 801; Like Ratio: 96%; Length: 16m
[Linear Algebra] Matrix-Vector Equation Ax=b Views: 73.3K; Net Likes: 449; Like Ratio: 96%; Length: 11m
Chapter 1.4: Matrix Equation Ax = b
[Linear Algebra] Matrix-Vector Equation Ax=b Views: 73.3K; Net Likes: 449; Like Ratio: 96%; Length: 11m
Solving Ax=b Views: 12.9K; Net Likes: 153; Like Ratio: 97%; Length: 9m
Linear Algebra - Lecture 9 - Matrix Equations Views: 8.58K; Net Likes: 91; Like Ratio: 100%; Length: 18m
Linear Algebra Example Problems - The Matrix Product Ax Views: 9.51K; Net Likes: 85; Like Ratio: 100%; Length: 6m
Chapter 1.5: Solution Sets of Linear Systems
Elimination Method For Solving Systems of Linear Equations Using Addition and Multiplication, Algebr Views: 152K; Net Likes: 1.69K; Like Ratio: 96%; Length: 10m
Linear Algebra Example Problems - General Solution of Augmented Matrix Views: 60.2K; Net Likes: 359; Like Ratio: 96%; Length: 8m
[Linear Algebra] Homogeneous Linear Systems and Parametric Form Views: 25.9K; Net Likes: 290; Like Ratio: 98%; Length: 10m
[Linear Algebra] Solution Sets for Systems of Equations Views: 33.3K; Net Likes: 288; Like Ratio: 98%; Length: 11m
Chapter 1.6: Applications of Linear Systems
Linear Algebra - Lecture 12 - Applications to Economics Views: 6.08K; Net Likes: 51; Like Ratio: 98%; Length: 5m
Linear Algebra - Lecture 14 - Applications to Networks Views: 3.49K; Net Likes: 34; Like Ratio: 100%; Length: 6m
Linear Algebra 1.6.1 Applications of Linear Systems - Economic Sectors Views: 767; Net Likes: 12; Like Ratio: 100%; Length: 6m
Elementary Linear Algebra Lecture 11 - Applications of linear systems (part 1) Views: 1.36K; Net Likes: 11; Like Ratio: 100%; Length: 23m
Chapter 1.7: Linear Independence
Introduction to linear independence | Vectors and spaces | Linear Algebra | Khan Academy Views: 856K; Net Likes: 2.09K; Like Ratio: 97%; Length: 15m
Span and linear independence example | Vectors and spaces | Linear Algebra | Khan Academy Views: 620K; Net Likes: 1.31K; Like Ratio: 96%; Length: 16m
More on linear independence | Vectors and spaces | Linear Algebra | Khan Academy Views: 470K; Net Likes: 1.18K; Like Ratio: 98%; Length: 17m
Linear Algebra Example Problems - Linearly Independent Vectors #1 Views: 70.2K; Net Likes: 544; Like Ratio: 97%; Length: 4m
Chapter 1.8: Linear Transformations
Linear Transformations , Example 1, Part 1 of 2 Views: 566K; Net Likes: 2.53K; Like Ratio: 97%; Length: 9m
30. Linear Transformations and Their Matrices Views: 238K; Net Likes: 1.23K; Like Ratio: 98%; Length: 49m
Linear transformations as matrix vector products | Linear Algebra | Khan Academy Views: 394K; Net Likes: 997; Like Ratio: 97%; Length: 17m
Linear Algebra Example Problems - Finding "A" of a Linear Transformation #2 Views: 97.8K; Net Likes: 521; Like Ratio: 96%; Length: 7m
Chapter 1.9: Matrix of a Linear Transformation
Linear Algebra - Matrix Transformations Views: 240K; Net Likes: 4.28K; Like Ratio: 97%; Length: 19m
30. Linear Transformations and Their Matrices Views: 238K; Net Likes: 1.23K; Like Ratio: 98%; Length: 49m
Linear transformations as matrix vector products | Linear Algebra | Khan Academy Views: 394K; Net Likes: 997; Like Ratio: 97%; Length: 17m
Linear Algebra Example Problems - Finding "A" of a Linear Transformation #2 Views: 97.8K; Net Likes: 521; Like Ratio: 96%; Length: 7m
Chapter 2
Chapter 2.1: Matrix Operations
Matrix Operations Views: 235K; Net Likes: 872; Like Ratio: 97%; Length: 5m
Multiplying a matrix by a matrix | Matrices | Precalculus | Khan Academy Views: 778K; Net Likes: 657; Like Ratio: 98%; Length: 5m
Algebra 53 - Elementary Row Operations Views: 42.2K; Net Likes: 529; Like Ratio: 98%; Length: 10m
Matrix vector products | Vectors and spaces | Linear Algebra | Khan Academy Views: 265K; Net Likes: 481; Like Ratio: 97%; Length: 21m
Chapter 2.2: Inverse of a Matrix
Idea behind inverting a 2x2 matrix | Matrices | Precalculus | Khan Academy Views: 1.21M; Net Likes: 3.54K; Like Ratio: 97%; Length: 14m
Inverse of a 2x2 matrix | Matrices | Precalculus | Khan Academy Views: 804K; Net Likes: 2.45K; Like Ratio: 96%; Length: 2m
Classic video on inverting a 3x3 matrix part 1 | Matrices | Precalculus | Khan Academy Views: 735K; Net Likes: 2.4K; Like Ratio: 96%; Length: 16m
Inverse Matrix Using Gauss-Jordan / Row Reduction , Example 1 Views: 344K; Net Likes: 1.53K; Like Ratio: 96%; Length: 5m
Chapter 2.3: Characterizations of Invertible Matrices
Invertible matrix Views: 4.39K; Net Likes: 149; Like Ratio: 96%; Length: 2m
Invertible matrices are square Views: 3.24K; Net Likes: 140; Like Ratio: 99%; Length: 16m
invertible matrix theorem Views: 6.06K; Net Likes: 60; Like Ratio: 98%; Length: 7m
Linear Algebra - Lecture 25 - The Invertible Matrix Theorem Views: 6.85K; Net Likes: 56; Like Ratio: 98%; Length: 12m
Chapter 2.4: Matrix Factorizations
Dear linear algebra students, This is what matrices (and matrix manipulation) really look like Views: 197K; Net Likes: 8.09K; Like Ratio: 99%; Length: 16m
LU Decomposition - Shortcut Method Views: 393K; Net Likes: 3.24K; Like Ratio: 98%; Length: 9m
Solve a System of Linear Equations Using LU Decomposition Views: 291K; Net Likes: 2.51K; Like Ratio: 98%; Length: 8m
LU Decomposition | MIT 18.06SC Linear Algebra, Fall 2011 Views: 169K; Net Likes: 1.16K; Like Ratio: 96%; Length: 9m
Chapter 2.5: Dimension and Rank
Basis and Dimension | MIT 18.06SC Linear Algebra, Fall 2011 Views: 348K; Net Likes: 3.12K; Like Ratio: 97%; Length: 8m
Dimension of the column space or rank | Vectors and spaces | Linear Algebra | Khan Academy Views: 385K; Net Likes: 1.29K; Like Ratio: 98%; Length: 12m
Dimension of the null space or nullity | Vectors and spaces | Linear Algebra | Khan Academy Views: 293K; Net Likes: 801; Like Ratio: 97%; Length: 13m
[Linear Algebra] Dimension Views: 23.7K; Net Likes: 164; Like Ratio: 97%; Length: 11m
Chapter 2.6: Application of Matrices in Computer Graphics
Dear linear algebra students, This is what matrices (and matrix manipulation) really look like Views: 197K; Net Likes: 8.09K; Like Ratio: 99%; Length: 16m
The True Power of the Matrix (Transformations in Graphics) - Computerphile Views: 455K; Net Likes: 7.53K; Like Ratio: 96%; Length: 14m
Linear Algebra - Transformation Matrix for Scaling 2D Objects Views: 22.1K; Net Likes: 151; Like Ratio: 97%; Length: 19m
Computer Graphics and Matrices (90s style) Views: 7.64K; Net Likes: 104; Like Ratio: 98%; Length: 9m
Chapter 3
Chapter 3.1: Introduction to Determinants
3 x 3 determinant | Matrix transformations | Linear Algebra | Khan Academy Views: 386K; Net Likes: 1.16K; Like Ratio: 97%; Length: 10m
n x n determinant | Matrix transformations | Linear Algebra | Khan Academy Views: 337K; Net Likes: 1.05K; Like Ratio: 96%; Length: 18m
Engineering Mathematics | Linear Algebra (Determinants) Views: 28.8K; Net Likes: 480; Like Ratio: 97%; Length: 48m
Matrices - Properties of Determinants(Part 1) Views: 41K; Net Likes: 383; Like Ratio: 96%; Length: 2m
Chapter 3.2: Properties of Determinants
18. Properties of Determinants Views: 239K; Net Likes: 1.34K; Like Ratio: 99%; Length: 49m
3 x 3 determinant | Matrix transformations | Linear Algebra | Khan Academy Views: 386K; Net Likes: 1.16K; Like Ratio: 97%; Length: 10m
Properties of Determinants | MIT 18.06SC Linear Algebra, Fall 2011 Views: 76.3K; Net Likes: 507; Like Ratio: 97%; Length: 9m
Matrices - Properties of Determinants(Part 1) Views: 41K; Net Likes: 383; Like Ratio: 96%; Length: 2m
Chapter 3.3: Cramer's Rule, Volume, and Linear Transformations
20. Cramer's Rule, Inverse Matrix, and Volume Views: 212K; Net Likes: 922; Like Ratio: 98%; Length: 51m
Cramer's Rule - 3x3 Linear System Views: 93.4K; Net Likes: 868; Like Ratio: 96%; Length: 15m
Linear Algebra 3.3 Determinants, Area and Volume Views: 21.8K; Net Likes: 169; Like Ratio: 96%; Length: 14m
14. Low Rank Changes in A and Its Inverse Views: 9.15K; Net Likes: 95; Like Ratio: 98%; Length: 50m
Chapter 4
Chapter 4.1: Vectors Spaces and Subspaces
What is a Vector Space? (Abstract Algebra) Views: 406K; Net Likes: 9.15K; Like Ratio: 99%; Length: 6m
Linear subspaces | Vectors and spaces | Linear Algebra | Khan Academy Views: 1.18M; Net Likes: 3.61K; Like Ratio: 97%; Length: 23m
Basis of a subspace | Vectors and spaces | Linear Algebra | Khan Academy Views: 941K; Net Likes: 2.31K; Like Ratio: 97%; Length: 19m
[Linear Algebra] Vector Spaces Views: 247K; Net Likes: 1.85K; Like Ratio: 96%; Length: 13m
Chapter 4.2: Null Spaces, Column Spaces, and Linear Transformations
Null space and column space basis | Vectors and spaces | Linear Algebra | Khan Academy Views: 586K; Net Likes: 1.79K; Like Ratio: 96%; Length: 25m
Null Space of a Vector Space Views: 143K; Net Likes: 1.28K; Like Ratio: 98%; Length: 8m
Null space 2: Calculating the null space of a matrix | Linear Algebra | Khan Academy Views: 511K; Net Likes: 1.06K; Like Ratio: 96%; Length: 13m
Introduction to the null space of a matrix | Vectors and spaces | Linear Algebra | Khan Academy Views: 499K; Net Likes: 803; Like Ratio: 96%; Length: 10m
Chapter 4.3: Linear Independent Sets; Bases
Independence, Basis, and Dimension Views: 191K; Net Likes: 3.3K; Like Ratio: 99%; Length: 13m
Basis for a Set of Vectors Views: 509K; Net Likes: 2.52K; Like Ratio: 96%; Length: 11m
Introduction to linear independence | Vectors and spaces | Linear Algebra | Khan Academy Views: 856K; Net Likes: 2.09K; Like Ratio: 97%; Length: 15m
Span and linear independence example | Vectors and spaces | Linear Algebra | Khan Academy Views: 620K; Net Likes: 1.31K; Like Ratio: 96%; Length: 16m
Chapter 4.4: Coordinate Systems
Rotation in R3 around the x-axis | Matrix transformations | Linear Algebra | Khan Academy Views: 186K; Net Likes: 480; Like Ratio: 97%; Length: 12m
Algebra 42 - Visualizing Linear Equations in Three Variables Views: 26.7K; Net Likes: 421; Like Ratio: 98%; Length: 10m
Linear Algebra Example Problems - Coordinate System Representation Example #1 Views: 30.6K; Net Likes: 214; Like Ratio: 96%; Length: 5m
Showing that an eigenbasis makes for good coordinate systems | Linear Algebra | Khan Academy Views: 112K; Net Likes: 196; Like Ratio: 98%; Length: 13m
Chapter 4.5: Rank
Dimension of the column space or rank | Vectors and spaces | Linear Algebra | Khan Academy Views: 385K; Net Likes: 1.29K; Like Ratio: 98%; Length: 12m
11. Matrix Spaces; Rank 1; Small World Graphs Views: 285K; Net Likes: 1.28K; Like Ratio: 99%; Length: 45m
Dimension of the null space or nullity | Vectors and spaces | Linear Algebra | Khan Academy Views: 293K; Net Likes: 801; Like Ratio: 97%; Length: 13m
rank(a) = rank(transpose of a) | Matrix transformations | Linear Algebra | Khan Academy Views: 104K; Net Likes: 174; Like Ratio: 95%; Length: 11m
Chapter 4.6: Change of Basis
Change of basis explained simply | Linear algebra makes sense Views: 21.8K; Net Likes: 736; Like Ratio: 97%; Length: 11m
Linear Algebra Example Problems - Change of Coordinates Matrix #2 Views: 60.1K; Net Likes: 682; Like Ratio: 98%; Length: 10m
Example of Change of Basis Views: 48.2K; Net Likes: 362; Like Ratio: 97%; Length: 7m
Linear Algebra Example Problems - Change of Coordinates Matrix #1 Views: 43.5K; Net Likes: 268; Like Ratio: 95%; Length: 8m
Chapter 5
Chapter 5.1: Eigenvectors and Eigenvalues
Introduction to Eigenvalues and Eigenvectors - Part 1 Views: 1.14M; Net Likes: 5.97K; Like Ratio: 97%; Length: 5m
Eigenvalue and Eigenvector Computations Example Views: 393K; Net Likes: 2.4K; Like Ratio: 96%; Length: 16m
Eigenvalues and Eigenvectors Views: 164K; Net Likes: 2.31K; Like Ratio: 99%; Length: 19m
Finding eigenvectors and eigenspaces example | Linear Algebra | Khan Academy Views: 771K; Net Likes: 1.01K; Like Ratio: 95%; Length: 14m
Chapter 5.2: Characteristic Equation
Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (5 of 35) What is an Eigenvector? Views: 7.87K; Net Likes: 77; Like Ratio: 99%; Length: 2m
Linear Algebra - Lecture 34 - The Characteristic Equation Views: 4.93K; Net Likes: 54; Like Ratio: 100%; Length: 13m
Linear Algebra - Eigenvalues and the Characteristic Equation Views: 49; Net Likes: 13; Like Ratio: 100%; Length: 49m
Linear Algebra 5.2.2 The Characteristic Equation Views: 602; Net Likes: 9; Like Ratio: 100%; Length: 8m
Chapter 5.3: Diagonalization
22. Diagonalization and Powers of A Views: 280K; Net Likes: 1.37K; Like Ratio: 99%; Length: 51m
Visualizing Diagonalization & Eigenbases Views: 9.74K; Net Likes: 291; Like Ratio: 98%; Length: 9m
Diagonalization Views: 8.51K; Net Likes: 228; Like Ratio: 98%; Length: 8m
The 4 Ways to Tell if a Matrix is Diagonalizable [Passing Linear Algebra] Views: 16.2K; Net Likes: 187; Like Ratio: 95%; Length: 8m
Chapter 5.4: Eigenvectors and Linear Transformations
30. Linear Transformations and Their Matrices Views: 238K; Net Likes: 1.23K; Like Ratio: 98%; Length: 49m
Finding eigenvectors and eigenspaces example | Linear Algebra | Khan Academy Views: 771K; Net Likes: 1.01K; Like Ratio: 95%; Length: 14m
Linear transformations as matrix vector products | Linear Algebra | Khan Academy Views: 394K; Net Likes: 997; Like Ratio: 97%; Length: 17m
[Linear Algebra] Linear Transformations Views: 37.6K; Net Likes: 347; Like Ratio: 97%; Length: 12m
Chapter 5.5: Complex Eigenvalues
Complex Eigenvalues Views: 40.7K; Net Likes: 461; Like Ratio: 96%; Length: 9m
Complex eigenvalues Views: 6.26K; Net Likes: 221; Like Ratio: 100%; Length: 21m
Linear Systems of DE with Complex Eigenvalues Views: 4.81K; Net Likes: 101; Like Ratio: 99%; Length: 24m
Complex Eigenvalues and Eigenvectors [Passing Linear Algebra] Views: 6.05K; Net Likes: 64; Like Ratio: 97%; Length: 13m
Chapter 6
Chapter 6.1: Inner Product, Length and Orthogonality
Inner Product and Orthogonal Functions , Quick Example Views: 162K; Net Likes: 665; Like Ratio: 97%; Length: 3m
Inner & outer products | Lecture 5 | Matrix Algebra for Engineers Views: 25.5K; Net Likes: 486; Like Ratio: 99%; Length: 9m
Linear Algebra - Lecture 37 - Inner Product, Length, and Orthogonality Views: 6.24K; Net Likes: 99; Like Ratio: 99%; Length: 12m
Linear Algebra - Inner Product, Vector Length, Orthogonality Views: 10.7K; Net Likes: 89; Like Ratio: 97%; Length: 7m
Chapter 6.2: Orthogonal Sets
Orthogonal sets Views: 4.93K; Net Likes: 203; Like Ratio: 99%; Length: 23m
linear algebra section 6.2 Orthogonal Sets Views: 7.94K; Net Likes: 70; Like Ratio: 97%; Length: 15m
Orthogonal Sets and Bases Views: 10.3K; Net Likes: 62; Like Ratio: 98%; Length: 11m
Linear Algebra - Lecture 38 - Orthogonal Sets Views: 4.12K; Net Likes: 47; Like Ratio: 96%; Length: 11m
Chapter 6.4: Gram-Schmidt Process
Gram Schmidt Method, Orthogonal and Orhonormal Basis Example Views: 122K; Net Likes: 986; Like Ratio: 95%; Length: 5m
Linear Algebra: Gram-Schmidt Views: 67.1K; Net Likes: 773; Like Ratio: 97%; Length: 13m
Gram-Schmidt example with 3 basis vectors | Linear Algebra | Khan Academy Views: 162K; Net Likes: 346; Like Ratio: 96%; Length: 13m
17. Orthogonal Matrices and Gram-Schmidt Views: 25.6K; Net Likes: 332; Like Ratio: 98%; Length: 49m
Chapter 6.5: Least-Sqaures Problem
Least squares approximation | Linear Algebra | Khan Academy Views: 325K; Net Likes: 1.16K; Like Ratio: 96%; Length: 15m
Least squares examples | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy Views: 221K; Net Likes: 573; Like Ratio: 97%; Length: 18m
9. Four Ways to Solve Least Squares Problems Views: 23K; Net Likes: 307; Like Ratio: 98%; Length: 49m
Linear Algebra and Optimization Seminar (CME 510) Views: 4.02K; Net Likes: 58; Like Ratio: 100%; Length: 1H16m
Chapter 7
Chapter 7.1: Diagonalization of Symmetric Matrices
Eigenvectors of Symmetric Matrices Are Orthogonal Views: 28K; Net Likes: 332; Like Ratio: 95%; Length: 11m
Linear Algebra - Lecture 41 - Diagonalization of Symmetric Matrices Views: 2.17K; Net Likes: 26; Like Ratio: 100%; Length: 15m
Diagonalization of Symmetric Matrices in Linear Algebra and Geometry Views: 85; Net Likes: 3; Like Ratio: 100%; Length: 9m
Linear Algebra - Diagonalization of Symmetric Matrices Views: 20; Net Likes: 1; Like Ratio: 100%; Length: 10m
Chapter 7.2: Quadratic Forms
Quadratic Forms Views: 16.4K; Net Likes: 540; Like Ratio: 98%; Length: 13m
Quadratic Form to Matrix form & Vice Versa Views: 7.26K; Net Likes: 127; Like Ratio: 96%; Length: 8m
Quadratic Forms and Principal Axes - Linear Algebra - F9 Views: 7.94K; Net Likes: 119; Like Ratio: 97%; Length: 26m
Quadratic Form: 3x3 Symmetric Matrix Views: 9.38K; Net Likes: 89; Like Ratio: 98%; Length: 6m
Chapter 7.3: Constrained Optimzation
Least squares approximation | Linear Algebra | Khan Academy Views: 325K; Net Likes: 1.16K; Like Ratio: 96%; Length: 15m
Constrained optimization introduction Views: 188K; Net Likes: 1.06K; Like Ratio: 97%; Length: 6m
Linear Programming Views: 94.2K; Net Likes: 1.01K; Like Ratio: 97%; Length: 33m
LP Graphical Method (Multiple/Alternative Optimal Solutions) Views: 72.6K; Net Likes: 854; Like Ratio: 97%; Length: 5m
Chapter 7.4: Singular Value Decomposition
Computing the Singular Value Decomposition | MIT 18.06SC Linear Algebra, Fall 2011 Views: 307K; Net Likes: 2.6K; Like Ratio: 96%; Length: 11m
6. Singular Value Decomposition (SVD) Views: 39.7K; Net Likes: 629; Like Ratio: 99%; Length: 53m
Singular Value Decomposition (SVD): Overview Views: 16.3K; Net Likes: 382; Like Ratio: 99%; Length: 6m
Gilbert Strang: Singular Value Decomposition Views: 7.1K; Net Likes: 277; Like Ratio: 99%; Length: 5m