Principal axis theorem
= Principal axis theorem
{wiki=Principal_axis_theorem}
The Principal Axis Theorem, often discussed in the context of linear algebra and quadratic forms, refers to a method of diagonalizing a symmetric matrix. This theorem states that for any real symmetric matrix, there exists an orthogonal matrix \\(Q\\) such that: \\\[ Q^T A Q = D \\\] where \\(A\\) is the symmetric matrix, \\(Q\\) is an orthogonal matrix (i.e.