ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
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Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
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Countable map
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Matrix
Real collection matrix
Complex matrix
Definition D5844
Complex matrix vectorization
Formulation 0
Let $A \in \mathbb{C}^{N \times M}$ be a D999: Complex matrix such that
(i) \begin{equation} A = \begin{bmatrix} A_{1, 1} & A_{1, 2} & \cdots & A_{1, M} \\ A_{2, 1} & A_{2, 2} & \vdots & A_{2, M} \\ \vdots & \cdots & \ddots & \vdots \\ A_{N, 1} & A_{N, 2} & \cdots & A_{N, M} \end{bmatrix} \end{equation}
The vectorization of $A$ is the D5689: Complex column matrix \begin{equation} \begin{bmatrix} A_{1, 1}, & \ldots, & A_{N, 1}, & A_{1, 2}, & \ldots, & A_{N, 2}, & \ldots, & A_{1, M}, & \ldots, & A_{N, M} \end{bmatrix} ^T \in \mathbb{C}^{NM \times 1} \end{equation}
Children
Real matrix vectorization