The Spectral Theorem for Finite Matrices and Cochran's Theorem

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

A Cayley-Hamiltonian Theorem for Periodic Finite Band Matrices

Let K be a doubly infinite, self–adjoint matrix which is finite band (i.e. Kjk = 0 if |j − k| > m) and periodic (KS = SK for some n where (Su)j = uj+1) and non–degenerate (i.e. Kjj+m 6= 0 for all j). Then, there is a polynomial, p(x, y), in two variables with p(K,S) = 0. This generalizes the tridiagonal case where p(x, y) = y − y∆(x) + 1 where ∆ is the discriminant. I hope Pavel Exner will enjo...

Birkhoff's Theorem for Panstochastic Matrices

Weyl’s Theorem for Operator Matrices

Weyl’s theorem for an operator says that the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. H. Weyl ([22]) discovered that this property holds for hermitian operators and it has been extended from hermitian operators to hyponormal operators and to Toeplitz operators by L. Coburn ([5]), and to sever...

The Spectral Theorem and Beyond

We here present the main conclusions and theorems from a first rigorous inquiry into linear algebra. Although some basic definitions and lemmas have been omitted so to keep this exposition decently short, all the main theorems necesary to prove and understand the spectral, or diagonalization, theorem are here presented. A special attention has been placed on making the proofs not only proofs of...