SYMMETRIC MATRICES AND QUADRATIC FORMS

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

Principal Axes How to Examples Exercise How to: Consider a quadratic form, q = dot(x, A*x). Assume that A has N distinct eigenvalues. Then the principal axes of the geometric figure generated by this quadratic form are exactly the eigenvectors of the matrix A. To understand a little bit better what this means, check out the next section where we work with quadratic forms in a familiar setting, R2.      Examples: Exercise: