ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D5939
Real matrix standard submatrix
Formulation 1
Let $A \in \mathbb{R}^{N \times M}$ be a D4571: Real 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 D4571: Real matrix \begin{equation} (\{ 1, \ldots, N \} \setminus \{ n \}) \times (\{ 1, \ldots, M \} \setminus \{ m \}), \quad (i, j) \mapsto A_{i, j} \end{equation}
Children
▶ D5940: Real square matrix standard minor