411 REFERENCE · Wikibooks
On 2D Inverse Problems/Spectral properties
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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.