Linear Algebra and Matrix Theory
( 25 Modules )

Module #1
Introduction to Linear Algebra
Overview of linear algebra, importance, and applications

Module #2
Vector Operations
Basic vector operations, including addition, scalar multiplication, and norm

Module #3
Vector Spaces
Definition and properties of vector spaces, including subspace and span

Module #4
Linear Independence and Span
Linear independence, span, and basis of a vector space

Module #5
Matrix Operations
Basic matrix operations, including addition, scalar multiplication, and matrix multiplication

Module #6
Matrix Properties
Properties of matrices, including transpose, inverse, and determinant

Module #7
Linear Transformations
Definition and properties of linear transformations, including kernel and image

Module #8
Matrix Representations
Matrix representations of linear transformations, including matrix-vector product

Module #9
Eigenvalues and Eigenvectors
Definition and properties of eigenvalues and eigenvectors, including diagonalization

Module #10
Diagonalization of Matrices
Diagonalization of matrices, including eigenvalue decomposition

Module #11
Orthogonality and Orthonormality
Orthogonality and orthonormality of vectors and matrices

Module #12
Gram-Schmidt Process
Gram-Schmidt process for orthogonalization and orthonormalization

Module #13
Determinants
Definition and properties of determinants, including Cramers rule

Module #14
Inverse of a Matrix
Existence and uniqueness of inverse, including formulae and computations

Module #15
Linear Systems
Linear systems of equations, including solution methods and applications

Module #16
LU, Cholesky, and QR Decompositions
LU, Cholesky, and QR decompositions of matrices, including applications

Module #17
Singular Value Decomposition (SVD)
Singular value decomposition (SVD) of matrices, including applications

Module #18
Markov Chains and Transition Matrices
Markov chains and transition matrices, including steady-state distributions

Module #19
Linear Programming
Introduction to linear programming, including formulation and solution methods

Module #20
Applications of Linear Algebra
Applications of linear algebra in computer science, physics, engineering, and data analysis

Module #21
Computer Graphics and Linear Algebra
Applications of linear algebra in computer graphics, including transformations and projections

Module #22
Data Analysis and Linear Algebra
Applications of linear algebra in data analysis, including PCA and clustering

Module #23
Numerical Methods in Linear Algebra
Numerical methods for solving linear algebra problems, including iterative methods

Module #24
Linear Algebra and Machine Learning
Applications of linear algebra in machine learning, including neural networks and deep learning

Module #25
Course Wrap-Up & Conclusion
Planning next steps in Linear Algebra and Matrix Theory career

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Linear Algebra and Matrix Theory ( 25 Modules )

Linear Algebra and Matrix Theory
( 25 Modules )