Unit III: Positive Definite Matrices and Applications

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Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang

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.

Further Study

The Java® Demos below were developed by Professor Pavel Grinfeld and will be useful for a review of concepts covered throughout this unit.


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