Characteristic Polynomials and Eigenvalues for Certain Classes of Pentadiagonal Matrices

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