With reference to The Matrix Cookbook

0.1 Notation and Nomenclature

Notations

$\boldsymbol{A}$

$\boldsymbol{A}_{ij}$

$\boldsymbol{A}_i$

$\boldsymbol{A}^{ij}$

$\boldsymbol{A}^{n}$

$\boldsymbol{A}^{-1}$

$\boldsymbol{A}^{+}$

$\boldsymbol{A}^{1/2}$

$(\boldsymbol{A})_{ij}$

$\boldsymbol{A}_{ij}$

$[\boldsymbol{A}]_{ij}$

$\boldsymbol{a}$

$\boldsymbol{a}_i$

$a_i$

$a$

$\mathfrak{R}z$

$\mathfrak{R}\boldsymbol{z}$

$\mathfrak{R}\boldsymbol{Z}$

$\mathfrak{F}z$

$\mathfrak{F}\boldsymbol{z}$

$\mathfrak{F}\boldsymbol{Z}$

$\det(\boldsymbol{A})$

$\text{Tr}(\boldsymbol{A})$

$\text{diag}(\boldsymbol{A})$

$\text{eig}(\boldsymbol{A})$

$\text{vec}(\boldsymbol{A})$

$\text{sup}$

$||\boldsymbol{A}||$

$\boldsymbol{A}^\top$

$\boldsymbol{A}^{-\top}$

$\boldsymbol{A}^{*}$

$\boldsymbol{A}^H$

$\boldsymbol{A}\circ\boldsymbol{B}$

$\boldsymbol{A}\otimes\boldsymbol{B}$

$\boldsymbol{0}$

$\boldsymbol{I}$

$\boldsymbol{J}^{ij}$

$\boldsymbol{\Sigma}$

$\boldsymbol{\Lambda}$

Nomenclature

Matrix

Matrix indexed for some purpose

Matrix indexed for some purpose

Matrix indexed for some purpose

Matrix indexed for some purpose or The n.th power od a square matrix

The inverse matrix of the matrix $\boldsymbol{A}$

The pseudo inverse matrix of the matrix (see sector Inverse/Pseudo Inverse)

The square root of a matrix (if unique), not elementwise

The $(i,j)$.th entry of the matrix $\boldsymbol{A}$

The $(i,j)$.th entry of the matrix $\boldsymbol{A}$

The $ij$-submatrix, i.e. $\boldsymbol{A}$ with i.th row and j.th column deleted.

Vector (column-vector)

Vector indexed for some purpose

The i.th element of the vector $\boldsymbol{a}$

Scalar

Real part of a scalar

Real part of a vector

Real part of a matrix

Imaginary part of a scalar

Imaginary part of a vector

Imaginary part of a matrix

Determinant of $\boldsymbol{A}$

Trace of the matrix $\boldsymbol{A}$

Diagonal matrix of the matrix $\boldsymbol{A}$

Eigenvalues of the matrix $\boldsymbol{A}$

The vector-version of the matrix $\boldsymbol{A}$ (see section Functions and Operators/Kronecker and Vec Operator)

Supremum of a set

Matrix norm (subscript if any denotes what norm)

Transposed matrix

The inverse of the transposed and vice versa

Complex conjugated matrix

Transposed and complex conjugated matrix (Hermitian)

Hadamard (elementwise) product

Kronecker product

The null matrix. Zero in all entries.

The identity matrix

The single-entry matrix, $1$ at $(i, j)$ and zero elsewhere

A positive definite matrix

A diagonal matrix