Definition
The adjugate of A is the transpose of the cofactor matrix C of A:
- .
Verbose definition goes as: suppose R is a commutative ring and A is an n×n matrix with entries from R.
- Calculate the (i,j) minor of A, denoted Mij, as the determinant of the (n − 1)×(n − 1) matrix that results from deleting row i and column j of A.
- Calculate the cofactor matrix of A, as the n×n matrix C whose (i,j) entry is the (i,j) cofactor of A.
That is, the adjugate of A is the n×n matrix whose (i,j) entry is the (j,i) cofactor of A:
- .
If A is invertible,
- .
Read more about this topic: Adjugate Matrix
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