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Table of Contents
Basics
Trace and Determinants
The Special Case 2x2
Derivatives
Derivatives of a Determinant
Derivatives of an Inverse
Derivatives of Eigenvalues
Derivatives of Matrices, Vectors and Scalar Forms
Derivatives of Traces
Derivatives of vector norms
Derivatives of matrix norms
Derivatives of Structured Matrices
Inverses
Basic
Exact Relations
Implication on Inverses
Approximations
Generalized Inverse
Pseudo Inverse
Complex Matrices
Complex Derivatives
Higher order and non-linear derivatives
Inverse of complex sum
Solutions and Decompositions
Solutions to linear equations
Eigenvalues and Eigenvectors
Singular Value Decomposition
Triangular Decomposition
LU decomposition
LDM decomposition
LDL decompositions
Statistics and Probability
Definition of Moments
Expectation of Linear Combinations
Weighted Scalar Variable
Multivariate Distributions
Cauchy
Dirichlet
Normal
Normal-Inverse Gamma
Gaussian
Multinomial
Student's t
Wishart
Wishart, Inverse
Gaussians
Basics
Moments
Miscellaneous
Mixture of Gaussians
Special Matrices
Block matrices
Discrete Fourier Transform Matrix, The
Hermitian Matrices and skew-Hermitian
Idempotent Matrices
Orthogonal matrices
Positive Definite and Semi-definite Matrices
Singleentry Matrix, The
Symmetric, Skew-symmetric/Antisymmetric
Toeplitz Matrices
Transition matrices
Units, Permutation and Shift
Vandermonde Matrices
Functions and Operators
Functions and Series
Kronecker and Vec Operator
Vector Norms
Matrix Norms
Rank
Integral Involving Dirac Delta Functions
Miscellaneous
One-dimensional Results
Gaussian
One Dimensional Mixture of Gaussians
Proofs and Details
Misc Proofs