### Kronecker Product Every element in the first matrix times every element in the second in a certain order $ \begin{pmatrix} a_{11} & a_{12} & \dots \\ a_{21} & a_{22} & \dots \\ \vdots & \vdots \end{pmatrix} ⊗B = \begin{pmatrix} a_{11}B & a_{12}B & \dots \\ a_{21}B & a_{22}B & \dots \\ \vdots & \vdots \end{pmatrix} $ - A is mxn - B is pxq - A⊗B is mp x nq - $A⊗B \neq B⊗A$ **Vectorization** $\mathrm{vec}\,A=\mathrm{vec}\otimes\underbrace{\left(\begin{array}{c c c c}{{{\vec{a}}_{1}}}&{{{\vec{a}}_{2}}}&{{\cdot\cdot\cdot}}&{{{\vec{a}}_{n}}}\end{array}\right)}_{A\in\mathbb{R}^{m\times n}}=\left(\begin{array}{c}{{{\vec{a}}_{1}}}\\ {{{\vec{a}}_{2}}}\\ {{\vdots}}\\ {{{\vec{a}}_{n}}}\end{array}\right)\in\mathbb{R}^{m n}$ **Matrix Notation** ${} (A⊗B)*\mathrm{vec}~C = \mathrm{vec}(BCA^{T}) {}$ **Linear operator notation** $(A⊗B)[C] = BCA^{T}$