ThmDex – An index of mathematical definitions, results, and conjectures.
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▼ Real matrix standard submatrix
▼ Real square matrix standard minor
Definition D5941
Real square matrix cofactor
Formulation 1
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that
(i) $N \in \{ 2, 3, 4, \ldots \}$ is a D5094: Positive integer
(ii) $n, m \in \{ 1, 2, \ldots, N \}$ are each a D5094: Positive integer
(iii) $B \in \mathbb{R}^{(N - 1) \times (N - 1)}$ is a D5939: Real matrix standard submatrix for $A$ with respect to $(n, m)$
The cofactor for $A$ with respect to $(n, m)$ is the D993: Real number \begin{equation} (-1)^{n + m} \text{Det} B \end{equation}
Children
▶ D5942: Real cofactor matrix
Results
▶ R5509: Cofactor partition for the determinant of a 3-by-3 real square matrix
▶ R5063: Cofactor partition for the determinant of a real square matrix