Method on @sym: Lambda = eig (A) ¶

Method on @sym: [V, D] = eig (A) ¶

Symbolic eigenvalues/eigenvectors of a matrix.

Example:

A = sym([2 4; 6 8]);
sort(eig(A))
  ⇒ ans = (sym 2×1 matrix)
      ⎡5 - √33⎤
      ⎢       ⎥
      ⎣5 + √33⎦

We can also compute the eigenvectors:

[V, D] = eig(A)
  ⇒ V = (sym 2×2 matrix)
      ⎡  √33   1    1   √33⎤
      ⎢- ─── - ─  - ─ + ───⎥
      ⎢   6    2    2    6 ⎥
      ⎢                    ⎥
      ⎣    1          1    ⎦
  ⇒ D = (sym 2×2 matrix)
      ⎡5 - √33     0   ⎤
      ⎢                ⎥
      ⎣   0     5 + √33⎦

The eigenvectors are the columns of V; we can extract one and check:

v = V(:, 1)
  ⇒ v = (sym 2×1 matrix)
      ⎡  √33   1⎤
      ⎢- ─── - ─⎥
      ⎢   6    2⎥
      ⎢         ⎥
      ⎣    1    ⎦
lambda = D(1,1)
  ⇒ lambda = (sym) 5 - √33

simplify(A*v - lambda*v)
  ⇒ ans = (sym 2×1 matrix)
      ⎡0⎤
      ⎢ ⎥
      ⎣0⎦

Note: the generalized eigenvalue problem is not yet supported.

See also: @@sym/svd.

Package: symbolic