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User:DVD206/Spectral properties

< User:DVD206(Redirected from User:Daviddaved/Spectral properties)

The spectrum of a square totally positive matrix is simple. That is, all 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.