Linear Algebra
( 24 Modules )

Module #1
Introduction to Linear Algebra
Overview of the course, importance of linear algebra, and basic concepts

Module #2
Vector Operations
Addition, scalar multiplication, and basic properties of vectors

Module #3
Vector Spaces
Definition, examples, and properties of vector spaces

Module #4
Subspaces
Definition, examples, and properties of subspaces

Module #5
Span and Basis
Span of a set of vectors, basis of a vector space, and basis theorems

Module #6
Linear Independence
Definition, examples, and tests for linear independence

Module #7
Dimension and Rank
Dimension of a vector space, rank of a matrix, and relationships between them

Module #8
Matrix Operations
Addition, scalar multiplication, and matrix multiplication

Module #9
Inverse and Determinant of a Matrix
Definition, properties, and calculations of inverse and determinant of a matrix

Module #10
Linear Transformations
Definition, examples, and properties of linear transformations

Module #11
Matrix Representations of Linear Transformations
Matrix representations of linear transformations and their properties

Module #12
Eigenvalues and Eigenvectors
Definition, calculation, and properties of eigenvalues and eigenvectors

Module #13
Diagonalization of Matrices
Diagonalization of matrices, diagonalizability, and applications

Module #14
Orthogonality and Orthonormality
Orthogonal and orthonormal vectors, Gram-Schmidt process, and orthogonal projections

Module #15
Orthogonal Matrices and QR Decomposition
Orthogonal matrices, QR decomposition, and applications

Module #16
Linear Systems and Row Operations
Linear systems, row operations, and solving systems using Gaussian elimination

Module #17
Null Space and Column Space
Null space and column space of a matrix, and relationships between them

Module #18
Image and Kernel
Image and kernel of a linear transformation, and relationships between them

Module #19
Singular Value Decomposition (SVD)
Definition, properties, and applications of SVD

Module #20
Markov Chains and PageRank
Introduction to Markov chains, PageRank algorithm, and applications

Module #21
Computer Graphics and Linear Algebra
Applications of linear algebra in computer graphics

Module #22
Machine Learning and Linear Algebra
Applications of linear algebra in machine learning

Module #23
Statistics and Linear Algebra
Applications of linear algebra in statistics

Module #24
Course Wrap-Up & Conclusion
Planning next steps in Linear Algebra career

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