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.