Notation

Vectors are small letters. Matrices are capital letters.

Matrix notation

Dimensions

$A=[a_{ij}]$ is mn matrix: $\in C^{m\times n}$. $q=min\{m,n\}$. Square A: $m\times m$. $\hat{A}$ is rectangular.

Matrices related to A

$(v_1,v_2\dots )$ is a column vector v.

$a_i$: ith element of vector a or ith column of A. $a_i^{\ast }$: by context: ith row of $A$ or transpose of $a_i$. $A_{k+1:m,k:f}$: a submatrix; other unambiguous matlab notations $A_{i,:}$ for ith row etc.. $a_{i,j}$ an element of A. $A_{i,j}$: by context: an element of $A$ or a submatrix of A.

Conjugate matrix $\overline{A}$. Adjoint (Hermitian conjugate) of A: $A^{\ast }=\overline{A^T}$. $\tilde{A}$: $A$ as stored on computer; or as calculated by alg.

Dilation of matrix A: add rows and cols to A.

Special matrices

Permutation matrix, P. Lower triangular matrix L. Upper triangular matrix U. Diagonal matrix $D=diag(d_i)=diag(d)$. Orthogonal (or Orthonormal) matrix Q, $\hat{Q}$. Identity I.

Special vectors

ith col of I: $e_i$ (Canonical unit vector). e or 1: col vector of 1’s. $P_{\perp q}$: projector to space $\perp q$.

Abused notation

$y=O(ϵ)⟹\mathrm{\exists }c=f(m,n),\mathrm{\forall }x\underset{{ϵ}_M\to 0}{lim}y\le c{ϵ}_M$. Extra Defn: If $y=\frac{a(x)}{b(x)}$, at $b(x)=0$, $y=O(ϵ)$ means $a(x)=O(ϵb(x))$.