Positive definite and semidefinite: graphs of x'Ax.
In this unit we discuss matrices with special properties – symmetric, possibly complex, and positive definite. The central topic of this unit is converting matrices to nice form (diagonal or nearly-diagonal) through multiplication by other matrices. Generally, this process requires some knowledge of the eigenvectors and eigenvalues of the matrix.
The Java® Demos below were developed by Professor Pavel Grinfeld and will be useful for a review of concepts covered throughout this unit.