The adjugate, , of an matrix , is the matrix
where is the indicated minor of (the determinant obtained by deleting row and column from ). The adjugate is also known as the classical adjoint, to distinguish it from the usual usage of “adjoint” (http://planetmath.org/AdjointEndomorphism) which denotes the conjugate transpose operation.
The equivalence of (1) and (2) follows easily from the multi-linearity properties (http://planetmath.org/DeterminantAsAMultilinearMapping) of the determinant. Thus, the adjugate operation is closely related to the matrix inverse. Indeed, if is invertible, the adjugate can be defined as
Yet another definition of the adjugate is the following:
The adjugate operation enjoys a number of notable properties:
|Date of creation||2013-03-22 13:09:42|
|Last modified on||2013-03-22 13:09:42|
|Last modified by||rmilson (146)|