SYMMETRIC MATRICES AND QUADRATIC FORMS

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

Quadratic Forms How to Examples Exercise How to: When a student of mathematics hears the word quadratic, his or her mind should immediately think of the quadratic formula, which is used to solve polynomials of degree 2. Quadratic forms are similar in the sense that they also deal with equations of degree 2. The main difference here is that in a normal polynomial our input is a single variable x, but in a quadratic form, our input is a vector x, and the equation that results are linear combinations of xI*xJ, where I could equal J. Quadratic forms can be represented in MATLAB with the equation:      q = dot(x, A*x) OR equivalently      q = x'*A*x Here we require that A be a symmetric matrix.      Examples: Exercise: