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.
- Eigenvalues
- SVD (Singular Value Decomposition)
- Gaussian Elimination
- Determinants
- Gram-Schmidt = Orthogonalization
- Inner Product of Functions
- Sum of Fourier Series
- Sum of Trigonometric Series
- Gibbs Phenomenon
- Aliasing
- Column Spaces
- Least Squares
- Power Method