Abstract
This chapter studies the polynomial families of the form
where ℓ ∈ ℕ and
for some N ∈ ℕ*. These families are called matrix polynomials in most of the available literature. More precisely, the family \( \mathfrak{L} \) defined in (10.1) is said to be a matrix polynomial of order N and degree ℓ. The main goal of this chapter is to obtain a spectral theorem for matrix polynomials, respecting the spirit of the Jordan Theorem 1.2.1.
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© 2007 Birkhäuser Verlag AG
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(2007). The Spectral Theorem for Matrix Polynomials. In: Algebraic Multiplicity of Eigenvalues of Linear Operators. Operator Theory: Advances and Applications, vol 177. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8401-2_10
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DOI: https://doi.org/10.1007/978-3-7643-8401-2_10
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8400-5
Online ISBN: 978-3-7643-8401-2
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