Unitary Matrix  $$U^H=U^{-1}$$.  The columns are orthonormal.

Transpose denoted by $$A’$$. rows and columns are interchanged: $$a_{ij} \leftarrow a_{ji}$$

Symmetric Matrix  $$A=A’$$

Positive Definite Matrix  Symmetric matrix A such that $$x^TAx > 0 \quad \forall x \neq 0$$.  All eigenvalues of A are > 0.

Frobenius Norm

\left\|A\right\|=\sqrt{\sum_{i=1}^m\sum_{j=1}^n a_{ij}^2}

Orthonormal A set of vectors $$v_i$$ is orthonormal if they all have length 1 and are orthogonal to each other, that is, $$\langle v_i, v_j \rangle = v_i{\,’} v_j = 0$$ if $$i\neq j$$.

Singular Value Decomposition

A=USV’

where U has orthonormal columns and V has orthonormal rows, and S is diagonal and has non-negative entries. If $$A$$ is square, then $$U,V$$ are unitary.