Lecture 1 - Introduction to Linear Algebra and Matrices
Lecture 2 - Geometry of System of linear equations - Straight lines andplanes, Matrix Definitions
Lecture 3 - Some Interpretations to solutions of system of linear equations
Lecture 4 - Matrix Operations, Homogeneous system of equations
Lecture 5 - Matrix Operations, Homogeneous system of equations
Lecture 6 - Elementary Row Operations
Lecture 7 - Elementary Row operations - How do they work?
Lecture 8 - Determinant and Inverse of a matrix
Lecture 9 - Interpreting the inverse of a matrix
Lecture 10 - Cramer's rule
Lecture 11 - Points and Vectors in 2D
Lecture 12 - Vector Length and properties
Lecture 13 - Combining Vectors
Lecture 14 - Linearly Independent and Dependent vectors, Dot Product of vectors
Lecture 15 - Angle between two vectors, Orthogonal projections
Lecture 16 - Lines and Parametric Equations of lines, Linear Maps
Lecture 17 - Rotation, Shear and Projection transformations
Lecture 18 - Determinant of 2x2 matrix as Area of Parallelogram,Determinant of linear transformations
Lecture 19 - System of 2 linear equations in 2 unknowns from vector perspective
Lecture 20 - Eigenvalues and eigenvectors
Lecture 21 - Vectors in 3D, Linear combination of vectors in 3D
Lecture 22 - Projectionvector on another vector, line passing through origin, plane passing through origin
Lecture 23 - Area of a parallelogram in 3D, Cross product
Lecture 24 - Interpreting the cross-product, Properties of cross-product
Lecture 25 - Volume of a parallelepiped, Lines in 3D, Intersection of line and plane
Lecture 26 - Linear Maps in 3D - Scaling and Reflection
Lecture 27 - Linear Maps in 3D - Reflection about a plane, Shear
Lecture 28 - Rotation in 3D
Lecture 29 - Determinant and its properties
Lecture 30 - eigenvalues and eigenvectors in 3D
Lecture 31 - Linear systems in 3D and geometric perspective
Lecture 32 - Homogeneous system in 3D
Lecture 33 - LU Decomposition
Lecture 34 - Least Squares Solution, Gram-Schmidt Orthogonalization, QRDecomposition
Lecture 35 - Orthogonal Matrix, Linear Independence, eigenvalues and eigenvectors in 3D
Lecture 36 - Vector Space and Properties
Lecture 37 - Examples of vector spaces - Polynomial space, planes and lines through origin
Lecture 38 - Vector Subspaces and their geometry
Lecture 39 - Combining vectors in a vector space, Linear Independence
Lecture 40 - Span, Basis, Dimension of a vector space, Fourier Expansion
Lecture 41 - Homogeneous system of linear equations and null space of a matrix
Lecture 42 - Column Space of A
Lecture 43 - Subspaces associated matrix A transpose, Nullity, Rank
Lecture 44 - Orthogonal Complement of a subspace
Lecture 45 - Orientation of the four fundamental subspaces of a matrix A
Lecture 46 - System of linear equations with no solution - Inconsistent systems
Lecture 47 - Least squares solution, Pseudoinverse of A
Lecture 48 - Projection and Projection Matrices
Lecture 49 - Pseudoinverse of special matrices
Lecture 50 - Eigendecomposition
Lecture 51 - Eigensubspace and dimension
Lecture 52 - Real Symmetric matrix and properties
Lecture 53 - Eigenvalues and eigenvectors of real symmetric matrices
Lecture 54 - Effect of a real symmetric matrix - Geometric Interpretation
Lecture 55 - Spectral Theorem, Quadratic Forms
Lecture 56 - Singular Value Decomposition
Lecture 57 - Relationship between SVD and Eigen Decomposition
Lecture 58 - An Interpretation of SVD
Lecture 59 - Fourier Series and Transform through Linear Algebra
Lecture 60 - Practical Applications of Linear Algebra - 1
Lecture 61 - Practical Applications of Linear Algebra - 2
Lecture 62 - Summary and Credits
