{"product_id":"m-monic-operator-and-matrix-polynomials-spectral-properties-factorizations-and-companion-forms-3838129377","title":"m-Monic Operator- and Matrix Polynomials: Spectral Properties, Factorizations and Companion Forms","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 3838129377\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Hartanto, Niels\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\u003c\/p\u003e\u003cp\u003eIn this thesis, spectral properties of analytic, so called m-monic operator- and matrix functions are investigated. A major focus lies on polynomials with entrywise nonnegative matrix coefficients. Crucial for the investigation of this case is the introduction of a degree reduction generalizing the well known linearization of matrix polynomials via the first companion form. This allows the development of a condition for the existence of spectral factorizations via fixpoint iterations. m-monic matrix polynomials with entrywise nonnegative coefficients such that their sum is irreducible can have eigenvalues with a symmetry similar to the rotation invariance of peripheral eigenvalues of entrywise nonnegative irreducible matrices. The analysis of this symmetry involves the well known Perron-Frobenius theory as it does in the matrix case, as well as the study of an associated infinite graph. A numerical algorithm for the computation of spectral factorizations also is given. It is based on a version of a cyclic reduction method suited for a certain type of Markov chains.\u003c\/p\u003e","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":68174216626464,"sku":"NEW3838129377","price":96.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/51d7JjzA2VS.jpg?v=1794055242","url":"https:\/\/miakarts.com\/products\/m-monic-operator-and-matrix-polynomials-spectral-properties-factorizations-and-companion-forms-3838129377","provider":"Miakarts Books","version":"1.0","type":"link"}