Linear Algebra
»
Part 7: Applications
» Fibonacci Matrices
Vladimir Dobrushkin
https://math.uri.edu/~dobrush/
Linear Algebra with Mathematica
Introduction to Linear Algebra
Linear Algebra Software
Systems of Linear Equations
Vector Spaces
Matrices
Manipulation of Matrices
Solving Systems of Linear Equations
Gaussian Elimination
Reduced Row-Echelon Form
Linear Independence
Bases and Dimensions
Matrix Transformations
Exercises
Answers
Matrix Algebra
Determinats
Cofactors
Cramer's Rule
Partitioned Matrices
Elementary Matrices
Elimination:
A
=
LU
PLU Factorization
Reflection
Givens Rotation
Rank and Nullity
Special Matrices
Exercises
Answers
Vector Spaces
Subspaces
Examples of Spaces
Kernels or Null Spaces
Row and Column Spaces
Range and Cokernel
Four Subsets
Solving
A
x
=
b
Eigenspaces
Generalized Eigenvectors
Direct Sums
Exercises
Answers
Functions of Matrices
Characteristic Polynomials
Minimal Polynomials
Diagonalization
Sylvester Formula
The Resolvent Method
Polynomial Interpolation
Positive Matrices
Roots
Polar Factorization
Spectral Decomposition
SVD
Exercises
Answers
Eucledian Vector Spaces
Orthogonality
Orthogonal Sets
Self-adjoint Matrices
Cholesky decomposition
Unitary Matrices
Projection Operators
Gram--Schmidt Process
QR-decomposition
Least Square Approximation
Quadratic Forms
Exercises
Answers
Numerical Methods
Eigenvalues and Eigenvectors
Properties of Eigenvalues and Eigenvectors
Similarity and Diagonalization
Applications
GPS Problem
Graph Theory
Error Correcting Codes
Electric Circuits
Markov Chains
Cryptography
Hill's determinant
Wave-length Transfer Matrix
Computer Graphics
Linear Programming
Fibonacci Matrices
Discrete Fourier Transform
Fast Fourier Transform
Representations
Vector Representations
Matrix Representations
Change of Basis
Orthonormal Diagonalization
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
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X
Z
Reference
Free Materials
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GFDL License
Linear Programming