Function: adjoint (M) ¶

Numerical Classical Adjoint / Adjugate of a square matrix.

Note on Terminology: This function computes the “Classical Adjoint” / Adjugate of M. For the Conjugate Transpose / Hermitian adjoint (which is commonly referred to as the “Adjoint” in modern usage), see ‘@double/ctranspose’.

Example:

M = [-3 2 -5; -1 0 -2; 3 -4 1];
A = adjoint (M)
  ⇒ A =
       -8   18   -4
       -5   12   -1
        4   -6    2

And note the following equalities involving the Classical Adjoint A:

M * A
  ⇒ ans =
      -6   0   0
       0  -6   0
       0   0  -6

A * M
  ⇒ ans =
      -6   0   0
       0  -6   0
       0   0  -6

det (M) * eye (3)
  ⇒ ans =
    Diagonal Matrix

      -6   0   0
       0  -6   0
       0   0  -6

See also: @@sym/adjoint.

Package: symbolic