Linear algebra MOC

Adjugate matrix

The adjugate matrix $a d j 𝑇$ of a square matrix $𝑇 \in M 𝑛, 𝑛 (𝑅)$ is the transpose of its cofactor matrix $c o f 𝑇$ . #m/def/linalg

Properties

For $𝑇 \in 𝑀 𝑛, 𝑛 (𝑅)$ , we have

$(a d j 𝑇) 𝑇 = 𝑇 (a d j 𝑇) = (d e t 𝑇) 1 𝑛$ by the Laplace expansion of the matrix determinant

#state/stub | #lang/en | #SemBr