Open main menu

Wikibooks β

On 2D Inverse Problems/Spectral properties

< On 2D Inverse Problems

The spectrum of a square totally positive matrix is simple. That is, all of its eigenvalues are positive and have multiplicity 1.

Exercise 1 (***). Use the Perron-Frobenius theorem applied to the compound matrices of a totally positive matrix to prove the statement above.

The eigenvectors of totally positive matrix form Chebyshev system.