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CME 302 Numerical Linear Algebra
Class Notes 2025
Linear Algebra Bootcamp
Vector spaces
Dot Product and Vector Norms
Linear Transformations and Matrices
Matrix-Matrix Multiplications
Operator and Matrix Norms
The Sherman-Morrison-Woodbury Formula
The Determinant
The Trace of a Matrix
Orthogonal Matrices
Projections
Block Matrix Operations
The Four Fundamental Subspaces
Eigendecomposition
Normal matrices
Applications of Eigenvalues
Singular Value Decomposition
Eigenvalues and Singular Values
Summary of Matrix Decompositions
Solving Linear Systems
The LU Decomposition Algorithm
Existence and Uniqueness of LU Factorization
Floating-Point Numbers
LU Factorization with Row Pivoting
Cholesky Factorization
License for this book
Index