Cofactors and Adjugate or Adjoint of A Matrix
The (i,j) cofactor Cij of a square matrix A is just (−1)i + j times the corresponding (n − 1) × (n − 1) minor Mij:
- Cij = (−1)i + j Mij
The cofactor matrix of A, or matrix of A cofactors, typically denoted C, is defined as the n×n matrix whose (i,j) entry is the (i,j) cofactor of A.
The transpose of C is called the adjugate or classical adjoint of A. (In modern terminology, the "adjoint" of a matrix most often refers to the corresponding adjoint operator.) Adjugate matrices are used to compute the inverse of square matrices.
Read more about this topic: Minor (linear Algebra)
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