Characteristic Polynomials and Eigenvalues for Certain Classes of Pentadiagonal Matrices

María Alejandra Alvarez, André Ebling Brondani, Francisca Andrea Macedo França and Luis A. Medina C.
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María Alejandra Alvarez: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
André Ebling Brondani: Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal Fluminense, Volta Redonda 27213-145, RJ, Brazil
Francisca Andrea Macedo França: Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal Fluminense, Volta Redonda 27213-145, RJ, Brazil
Luis A. Medina C.: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

Mathematics, 2020, vol. 8, issue 7, 1-12

Abstract: There exist pentadiagonal matrices which are diagonally similar to symmetric matrices. In this work we describe explicitly the diagonal matrix that gives this transformation for certain pentadiagonal matrices. We also consider particular classes of pentadiagonal matrices and obtain recursive formulas for the characteristic polynomial and explicit formulas for their eigenvalues.

Keywords: pentadiagonal matrix; symmetric pentadiagonal matrix; eigenvalue; characteristic polynomial (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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