ThmDex – An index of mathematical definitions, results, and conjectures.
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▼ Real matrix standard submatrix
▼ Real square matrix standard minor
▼ Real square matrix cofactor
Definition D5942
Real cofactor matrix
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
The cofactor matrix for $A$ is the D6160: Real square matrix \begin{equation} \begin{bmatrix} \text{Cof}_A (1, 1) & \text{Cof}_A (1, 2) & \cdots & \text{Cof}_A (1, N) \\ \text{Cof}_A (2, 1) & \text{Cof}_A (2, 2) & \vdots & \text{Cof}_A (2, N) \\ \vdots & \cdots & \ddots & \vdots \\ \text{Cof}_A (N, 1) & \text{Cof}_A (N, 2) & \cdots & \text{Cof}_A (N, N) \end{bmatrix} \end{equation}
Children
▶ D5943: Real adjugate matrix
Results
▶ R5505: Cofactor matrix for a 2-by-2 real square matrix