SYMMETRIC MATRICES AND QUADRATIC FORMS

Orthogonally Diagonalizable Symmetric Matrices and Eigenvalues How to Orthogonally Diagonalize Quadratic Forms Definiteness Principal Axes Ellipses and Hyperbolas

Orthogonally Diagonalizable How to Examples Exercise How to: We say a matrix A is orthogonally diagonalizable if there exists an orthogonal matrix S such that inv(S)*A*S (equivalently S'*A*S since inv(S) == S' for all orthogonal matrices) is diagonal. As it turns out, A is orthogonally diagonalizable if and only if it is a symmetric matrix. You'll see how to orthogonally diagonalize a matrix after we introduce some new facts about symmetric matrices and eigenvalues.      Examples: Exercise: