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
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