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
Famous quotes containing the word definition:
“One definition of man is an intelligence served by organs.”
—Ralph Waldo Emerson (18031882)
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possessafter many mysterieswhat one loves.”
—François, Duc De La Rochefoucauld (16131680)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (17721834)