User:Rogério Brito/Books/Loose Topics in Linear Algebra

Topics in Linear Algebra

Some basics

Cauchy–Schwarz inequality

Steinitz exchange lemma

Rank (linear algebra)

Trace (linear algebra)

Trace inequality

Change of basis

Orthogonal complement

Projection (linear algebra)

Transpose

Rank-nullity theorem

Rank–nullity theorem

Up to the Spectral Theorem

Eigenvalues and eigenvectors

Eigendecomposition of a matrix

Defective matrix

Spectral theorem

Characteristic polynomial

Cayley–Hamilton theorem

Minimal polynomial (linear algebra)

Pseudo-inverse

Moore–Penrose inverse

Proofs involving the Moore–Penrose inverse

Factorizations

LU decomposition

QR decomposition

Rank factorization

Eigendecomposition of a matrix

Cholesky decomposition

Singular value decomposition

Polar decomposition

Transposes and Dual spaces

Transpose of a linear map

Bilinear form

Quadratic form

Definiteness of a matrix

Definiteness of a matrix

Square root of a matrix

Square root of a 2 by 2 matrix

Other spaces

Dual space

Direct sum of modules

Quotient space (linear algebra)

Special matrices

Symmetric matrix

Hermitian matrix

Normal matrix

Diagonalizable matrix

Skew-symmetric matrix

Orthogonal matrix

Extra topics in Linear Algebra

Determinant

Eigenvalue algorithm

Rayleigh quotient

Schur complement

Perron–Frobenius_theorem

Extra topics in General

Lagrange multiplier

Isomorphism theorems

Zassenhaus lemma

Correspondence theorem (group theory)

Spectral Graph Theory

Adjacency matrix

Incidence matrix

Laplacian matrix

Algebraic connectivity

Cheeger constant (graph theory)

Applications of Spectral Graph Theory

Spectral clustering

Expander graph

Cayley graph

Kirchhoff's theorem