ThmDex – An index of mathematical definitions, results, and conjectures.
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Deduction system
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Zermelo-Fraenkel set theory
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Binary cartesian set product
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Submatrix
Definition D6181
Complex matrix standard submatrix
Formulation 0
Let $A \in \mathbb{C}^{N \times M}$ be a D999: Complex matrix such that
(i) $N, M \in \{ 2, 3, 4, \ldots \}$ are each a D5094: Positive integer
(ii) $n \in \{ 1, \ldots, N \}$ is a D5094: Positive integer
(iii) $m \in \{ 1, \ldots, M \}$ is a D5094: Positive integer
The standard submatrix for $A$ with respect to $(n, m)$ is the D999: Complex matrix \begin{equation} (\{ 1, \ldots, N \} \setminus \{ n \}) \times (\{ 1, \ldots, M \} \setminus \{ m \}), \quad (i, j) \mapsto A_{i, j} \end{equation}
Children
Complex square matrix standard minor