ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Countable map
Array
Matrix
Submatrix
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