Method on @sym: orth (A) ¶

Orthonormal basis for column space (range) of symbolic matrix.

Examples:

A = sym([1 1; 2 0]);
orth (A)
  ⇒ (sym 2×2 matrix)

      ⎡ √5   2⋅√5⎤
      ⎢ ──   ────⎥
      ⎢ 5     5  ⎥
      ⎢          ⎥
      ⎢2⋅√5  -√5 ⎥
      ⎢────  ────⎥
      ⎣ 5     5  ⎦

A = sym([1 2; 1 2]);
orth (A)
  ⇒ ans = (sym 2×1 matrix)

      ⎡√2⎤
      ⎢──⎥
      ⎢2 ⎥
      ⎢  ⎥
      ⎢√2⎥
      ⎢──⎥
      ⎣2 ⎦

The basis is often not unique and in general double(orth(A)) may not match the output of orth(double(A)).

See also: @sym/rank, @sym/null, @sym/rref.

Package: symbolic