| symbol | latex code | explanation | |
|---|---|---|---|
A⊤ | A^\top | Matrix transpose | |
A⁻¹ | A^{-1} | Matrix inverse | |
det(A) | \det(A) | Matrix determinant | |
tr(A) | \text{tr}(A) | Matrix trace | |
rank(A) | \text{rank}(A) | Matrix rank | |
adj(A) | \text{adj}(A) | Matrix adjugate | |
A⊗B | A \otimes B | Kronecker product | |
A∘B | A \circ B | Hadamard (elementwise) product | |
A† | A^\dagger | Conjugate transpose | |
ker(A) | \text{ker}(A) | Kernel (nullspace) of matrix | |
ℝⁿ | \mathbb{R}^n | n-dimensional real vector space | |
span{v₁,...,vₙ} | \text{span}\{v_1,\ldots,v_n\} | Span of vectors | |
⟨v,w⟩ | \langle v,w \rangle | Inner product | |
∥v∥ | \|v\| | Vector norm | |
v⊥w | v \perp w | Orthogonal vectors | |
dim(V) | \dim(V) | Dimension of vector space | |
V⊕W | V \oplus W | Direct sum of vector spaces | |
Av=λv | Av=\lambda v | Eigenvalue equation | |
χₐ(λ) | \chi_A(\lambda) | Characteristic polynomial | |
σ(A) | \sigma(A) | Spectrum (set of eigenvalues) | |
ρ(A) | \rho(A) | Spectral radius | |
diag(λ₁,...,λₙ) | \text{diag}(\lambda_1,\ldots,\lambda_n) | Diagonal matrix of eigenvalues | |
T:V→W | T:V\to W | Linear transformation | |
im(T) | \text{im}(T) | Image of transformation | |
ker(T) | \text{ker}(T) | Kernel of transformation | |
T∘S | T \circ S | Composition of transformations | |
GL(n,ℝ) | GL(n,\mathbb{R}) | General linear group | |
A=LU | A=LU | LU decomposition | |
A=QR | A=QR | QR decomposition | |
A=UΣV⊤ | A=U\Sigma V^\top | Singular value decomposition | |
A=PDP⁻¹ | A=PDP^{-1} | Eigendecomposition | |
A=CC⊤ | A=CC^\top | Cholesky decomposition | |
[a₁₁ a₁₂; a₂₁ a₂₂] | \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} | 2×2 matrix | |
(a b c) | \begin{pmatrix} a & b & c \end{pmatrix} | Row vector | |
[a; b; c] | \begin{bmatrix} a \\ b \\ c \end{bmatrix} | Column vector | |
∥a₁₁ a₁₂∥ | \begin{vmatrix} a_{11} & a_{12} \end{vmatrix} | Matrix determinant notation | |
{a₁₁ a₁₂} | \begin{Bmatrix} a_{11} & a_{12} \end{Bmatrix} | Curly brace matrix | |
aᵢⱼ | a_{ij} | General matrix element | |
a₁₁ | a_{11} | First element | |
aᵢ₊₁,ⱼ | a_{i+1,j} | Element with offset indices | |
⋯ | \cdots | Horizontal ellipsis | |
⋮ | \vdots | Vertical ellipsis | |
⋱ | \ddots | Diagonal ellipsis | |
I | I_n | Identity matrix | |
0 | 0_{m \times n} | Zero matrix | |
diag(a₁,…,aₙ) | \text{diag}(a_1,\ldots,a_n) | Diagonal matrix | |
⎡⎢⎣ | \left\lbrack | Left matrix bracket | |
⎤⎥⎦ | \right\rbrack | Right matrix bracket |