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
Real cofactor matrix
Definition D5943
Real adjugate matrix
Formulation 0
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that
(i) $\text{Cof} A$ is a D5942: Real cofactor matrix for $A$
The adjugate matrix for $A$ is the D6160: Real square matrix \begin{equation} (\text{Cof} A)^T \end{equation}
Results
Adjugate for a 2-by-2 real square matrix
Expression for a real matrix inverse in terms of adjugate
Product of a real square matrix and its adjugate is a constant diagonal matrix