Linear Algebra
Part 1: Systems of Linear Equations ≫ Norm and distance
Linear Algebra with Mathematica
Introduction to Linear Algebra
Linear Algebra Software
Systems of Linear Equations
Introduction
Linear Systems
Vectors
Norm and distance
Dot product
Linear combinations
Matrices
Manipulation of matrices
Matrix norms
Gaussian elimination
Reduced Row-Echelon Form
Equation
A
x
=
b
Sensitivity of solutions
Plane transformations
Exercises
Answers
Matrix Algebra
Introduction
Matrix transformations
Determinants
Cofactors
Cramer's rule
Partitioned matrices
Elementary Matrices
Inverse matrices
Elimination:
A
=
LU
PLU factorization
Reflection
Givens rotation
Special matrices
Exercises
Answers
Vector Spaces
Introduction
Vector Spaces
Linear Independence
Bases and Dimensions
Coordinates and basis
Subspaces
Matrix Spaces
Row space
Range or Column Space
Rank
Null Spaces or Kernels
Dimension Theorems
Four Subspaces
Solving
A
x
=
b
Eigenspaces
Where are Eigenvalues?
Eigenvalues of
AB
and
BA
Generalized Eigenvectors
Direct Sums
Exercises
Answers
Euclidean Vector Spaces
Introduction
Orthogonality
Orthogonal Sets
Self-adjoint Matrices
Cholesky decomposition
Unitary Matrices
Projection Operators
Gram--Schmidt Process
QR-decomposition
Least Square Approximation
Quadratic Forms
Exercises
Answers
Functions of Matrices
Introduction
Characteristic Polynomials
Algebraic and Geometric Multiplicities
Minimal Polynomials
Diagonalization
Sylvester Formula
The Resolvent Method
Polynomial Interpolation
Positive Matrices
Roots
Polar Factorization
Spectral Decomposition
SVD
Exercises
Answers
Numerical Methods
Computer solves Systems of Linear Equations
Location of Eigenvalues
Power Method
Singular Value Decomposition
Iterative Method
Similarity and Diagonalization
Applications
GPS Problem
Graph Theory
Error Correcting Codes
Electric Circuits
Markov Chains
Cryptography
Wave-length Transfer Matrix
Computer Graphics
Linear Programming
Hill's Determinant
Fibonacci Matrices
Discrete Fourier Transform
Fast Fourier Transform
Miscellany
Vector Representations
Matrix Representations
Change of Basis
Orthonormal Diagonalization
Generalized Inverse
Preliminaries
Complex Number Operations
Sets
Polynomials
Polynomials and Matrices
Glossary
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Z
Reference
Free Materials
Books
GFDL License
Vectors
References:
Vector addition
Tea
Milk