Linear Algebra

• Notes
• Videos & Interactives
• Questions

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Vectors
Vectors 
Linear Dependence of Vectors 
Orthogonal Unit Vectors 
​Resolution of a Vector into Rectangular Components 
​Scalar Product / Dot Product 
​​Scalar and Vector Resolutes 

Transformations of the Plane
Matrix Transformation 
Linear Transformations of R² 
More Transformations of R² 
Inverse Transformations 
Transformation on Subsets of the Plane 
​Invariant Points and Lines 
Eigenvalues and Eigenvectors 
Determinant and Area 
Matrix Multiplication Proofs 

Vectors
Cross Product (GeoGebra Interactive)
​Normal Vector (GeoGebra Interactive)

Mathematics for Machine Learning (University of California, Berkeley Article)

​Systems of linear equations

• Using Matrix Algebra to Find an Intersection Point of 3 Planes (Joel Speranza Math Video)
• Gaussian Elimination Part 1 (Joel Speranza Math Video)
• Gaussian Elimination Part 2 Systems with Lines as Solutions (Joel Speranza Math Video)
• Gaussian Elimination Part 3: Systems Resulting in No Solution (Joel Speranza Math Video)
• Gaussian Elimination Part 4: Finding the Equation of a Plane resulting in an Intersection (Joel Speranza Math Video)
• Row operations for Gaussian Elimination on the TI NSPIRE Calculator (Joel Speranza Math Video)
• The Geometric Interpretation of Systems of Linear Equations in 2 & 3 Dimensions (Joel Speranza Math Video)

Gaussian Elimination Part 1 (Joel Speranza Math Video)

How to determine the geometrical arrangement of 3 planes (Maths in an Empty Classroom Video)
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Oxford Linear Algebra

• Elementary Row Operations (EROs) Explained (Tom Rocks Maths Video)
• How to find a Matrix Inverse using ERO’s (Elementary Row Operations) (Tom Rocks Maths Video)
• What is the Determinant Function for a Matrix? (Tom Rocks Maths Video)
• The Easiest Method to Calculate Determinants (Tom Rocks Maths Video)
• Eigenvalues and Eigenvectors Explained (Tom Rocks Maths Video)
• Spectral Theorem Proof (Tom Rocks Maths Video)
• What is a Vector Space? (Tom Rocks Maths Video)
• Subspace Test (Tom Rocks Maths Video)
• Basis, Spanning and Linear Independence (Tom Rocks Maths Video)
• Dimension Formula for Vector Spaces (Tom Rocks Maths Video)
• Linear Transformations Explained (Tom Rocks Maths Video)
• Rank Nullity Theorem (Tom Rocks Maths Video)
• Inner Product Space (Tom Rocks Maths Video)
• Gram-Schmidt Process (Tom Rocks Maths Video)

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Matrix Transformations
​Matrix Transformations (GeoGebra Interactive)
Transformations using Matrices (GeoGebra Interactive)
Visualising Matrix Transformations (GeoGebra Interactive)
Reflecting in the Line y=mx with Matrix Transformations (Joel Speranza Math Video)
Composition of Matrix Transformations (Joel Speranza Math Video)
Inverse Matrix Transformation (Joel Speranza Math Video)
Transforming Multiple Points using a Single Matrix (Joel Speranza Math Video)
Finding an Unknown Matrix of Transformation (Joel Speranza Math Video)
Transforming Relations using Matrices (Part 1) (Joel Speranza Math Video)
Transforming Relations using Matrices (Part 2) (Joel Speranza Math Video)
Transforming Relations using Matrices (Part 3) (Joel Speranza Math Video)
Eigenvectors of 2⨉2 Matrices: A Geometric Exploration (Sine of the Times Interactive)
Oxford Linear Algebra: Eigenvalues and Eigenvectors Explained (Tom Rocks Maths Video)
Invariant Lines of Matrix Transformations (GeoGebra Interactive)
Transformation Toy (Berkley Interactive)
Bases and Coordinates in R^2 (Berkley Interactive)
​The Matrix Arcade (Yizhe-Ang Interactive)
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The PageRank Algorithm (Zach Star Video)
The Applications of Matrices (Zach Star Video)
The Applications of Eigenvectors and Eigenvalues | What do these things really tell us? (Zach Star Video)
Dear Linear Algebra Students, This is What Matrices (and Matrix Manipulation) Really Look Like (Zach Star Video)

Linear Algebra Makes Sense

• Vectors Make Sense (Looking Glass Universe Video)
• Matrices, Matrix Multiplication and Linear Transformations (Looking Glass Universe Video)
• A Simple Condition for When the Matrix Inverse Exists (Looking Glass Universe Video)
• Change of Basis Explained Simply (Looking Glass Universe Video)
• The Meaning of the Dot Product (Looking Glass Universe Video)​

Essence of Linear Algebra

• Essence of Linear Algebra Preview (3Brown1Blue Video)
• Vectors, what even are they? (3Brown1Blue Video)
• Linear Combinations, Span, and Basis Vectors (3Brown1Blue Video)
• Linear Transformations and Matrices (3Brown1Blue Video)
• Matrix Multiplication as Composition (3Brown1Blue Video)
• Three-Dimensional Linear Transformations (3Brown1Blue Video)
• The Determinant (3Brown1Blue Video)
• Inverse Matrices, Column Space, and Null Space (3Brown1Blue Video)
• Nonsquare Matrices as Transformations between Dimensions (3Brown1Blue Video)
• Dot Products and Duality (3Brown1Blue Video)
• Cross Products (3Brown1Blue Video)
• Cross Products in the Light of Linear Transformations (3Brown1Blue Video)
• Cramer's Rule, Explained Geometrically (3Brown1Blue Video)
• Change of Basis (3Brown1Blue Video)
• Eigenvectors and Eigenvalues (3Brown1Blue Video)
• A quick trick for computing eigenvalues (3Brown1Blue Video)
• Abstract Vectors Spaces (3Brown1Blue Video)
• How (and why) to raise e to the power of a matrix (3Brown1Blue Video)

Determinants

• ❖ 3x3 Determinant Shortcut: Find the Determinant of a 3x3 Matrix (patrickJMT Video)
• Determinant of 4x4 Matrix (patrickJMT Video)
• Determinant of a Triangular Matrix (patrickJMT Video)
• Determinants of Triangular Matrices patrickJMT Video()

LU Factorisation 

• LU Matrix Factorization (patrickJMT Video)
• LU Matrix Factorization, Example 2 (patrickJMT Video)
• Ladder Networks, Circuits, Transfer Matrix, LU Factorizations (patrickJMT Video)

Diagonalisation

• Diagonalization / Diagonalizing a Matrix, Part 1 (patrickJMT Video)
• Diagonalization / Diagonalizing a Matrix, Part 2 (patrickJMT Video)
  

Reflecting a line in a plane (Tayub Majeed TM Maths Questions)
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Linear Algebra Done Right (4th Edition) (Sheldon Axler Textbook)