29
References
Computational Linear Algebra
Download PDF
Download ePub
Twitter
Facebook
LinkedIn
1
Computational Linear Algebra in
\(\mathbb{R}^n\)
2
Introduction
Python Labs and Interactive Pages
I. Linear Equations and Matrix Computation
3
From Equations to Linear Systems
4
Matrices, Vectors, and Augmented Systems
5
Row Reduction and Gauss–Jordan Elimination
6
Matrix Algebra and Matrix Multiplication
7
Inverses, Elementary Matrices, and the Invertible Matrix Theorem
II. Geometry of R^n
8
Vectors, Linear Combinations, and Span
9
Linear Independence, Bases, and Dimension
10
Subspaces of
\(\mathbb{R}^n\)
11
Coordinates and Change of Basis
III. Linear Transformations
12
Linear Transformations in
\(\mathbb{R}^n\)
13
Composition, Matrix Products, and Inverse Transformations
IV. Orthogonality, Approximation, and Data
14
Length, Distance, Dot Product, and Orthogonality
15
Orthogonal Projection
16
Gram–Schmidt, QR Factorization, and Numerical Orthogonality
17
Least Squares and Data Fitting
V. Determinants and Eigenvalues
18
Determinants and Volume
19
Eigenvalues and Eigenvectors
20
Diagonalization and Discrete Dynamical Systems
VI. Symmetry, Spectral Geometry, and the Gateway to AI
21
Orthogonal Matrices and Symmetric Matrices
22
Quadratic Forms and Optimization Geometry
23
Singular Values and the Singular Value Decomposition
24
Linear Algebra for Data and AI
Appendices
25
Formula Sheet
26
Python Reference for Computational Linear Algebra
27
Proof Techniques for Linear Algebra
28
Review Problems
29
References
29
References
28
Review Problems