Determinants and Inverses of Ppoeplitz and Ppankel matrices

Abstract

In this paper, we consider two kinds of special matrices, which are called Ppoeplitz matrix and Ppankel matrix. The idea of matrix transformation is used to compute the determinants and inverses of the Ppoeplitz matrix and the Ppankel matrix. We develop efficient formulas for inverting the Ppoeplitz matrix and the Ppankel matrix. Specifically, for inverting the Ppoeplitz matrix and the Ppankel matrix using our proposed formulas, which only 11 entries need to be calculated when n is even, only 12 entries need to be calculated when n is odd. An example is given to illustrate the formulas.

Keywords

• ppoeplitz matrix
• ppankel matrix
• pell-padovan sequence
• determinant
• inverse
• primary 15b05
• 15a15
• secondary 11b39