`adjoint`

Classical adjoint (adjugate) of a square matrix.

Category: Mathematics > Linear Algebra

Syntax

X = adjoint(A)

Returns the transpose of the cofactor matrix of A.

Description

The adjugate exists even when A is singular, unlike the inverse. When A is invertible, inv(A) equals adjoint(A)/det(A). For a 2-by-2 matrix [a b; c d] the adjugate is [d -b; -c a].

Input arguments

A: Square symbolic or numeric matrix.

Output arguments

X: Matrix satisfying A*X == det(A)*eye(n).

Example

Adjugate of a 2-by-2 matrix

A = sym([1 2; 3 4]);
X = adjoint(A)
A*X

Output

X = 
[ 4, -2]
[-3,  1]
ans = 
[-2,  0]
[ 0, -2]

Notes

In MATLAB, adjoint is the classical adjoint, not the conjugate transpose; use A' for that.

See also

det inv transpose rank