Method on @sym: adjoint (A) ¶

Adjoint/Adjugate of a symbolic square matrix.

Caution: This computes the Adjugate or “Classical Adjoint” of the matrix. For the Conjugate Transpose (which is commonly referred to the “Adjoint”), see ‘@sym/ctranspose’.

Example:

syms x
A = [x x^3; 2*x i];
X = adjoint(A)
  ⇒ X = (sym 2×2 matrix)
      ⎡        3⎤
      ⎢ ⅈ    -x ⎥
      ⎢         ⎥
      ⎣-2⋅x   x ⎦

And note the matrix adjugate X satisfies:

A*X - det(A)*eye(2)
  ⇒ ans = (sym 2×2 matrix)
      ⎡0  0⎤
      ⎢    ⎥
      ⎣0  0⎦

See also: @@sym/ctranspose.

Package: symbolic