Orthogonal diagonalization explained

In linear algebra, an orthogonal diagonalization of a normal matrix (e.g. a symmetric matrix) is a diagonalization by means of an orthogonal change of coordinates.[1]

The following is an orthogonal diagonalization algorithm that diagonalizes a quadratic form q(x) on

R

n by means of an orthogonal change of coordinates X = PY.[2]

\Delta(t).

\Delta(t)

.

λ

of A from step 2, find an orthogonal basis of its eigenspace.

R

n.

Then X = PY is the required orthogonal change of coordinates, and the diagonal entries of

PTAP

will be the eigenvalues

λ1,...,λn

which correspond to the columns of P.

References

Notes and References

  1. Book: Poole, D. . Linear Algebra: A Modern Introduction . Cengage Learning . 2010 . 978-0-538-73545-2 . nl . 12 November 2018 . 411.
  2. [Seymour Lipschutz]