On the Inverse Of General Cyclic Heptadiagonal and Anti-Heptadiagonal Matrices

TL;DR

This paper introduces symbolic algorithms for computing determinants and inverses of general cyclic heptadiagonal and anti-cyclic matrices, facilitating implementation in computer algebra systems.

Contribution

It presents new symbolic algorithms specifically designed for inverting and determining determinants of cyclic heptadiagonal matrices, extending prior recursive methods.

Findings

Algorithms are suitable for CAS implementation.

Illustrative example demonstrates effectiveness.

Provides a systematic approach for these matrix classes.

Abstract

In the current work, the author present a symbolic algorithm for finding the determinant of any general nonsingular cyclic heptadiagonal matrices and inverse of anti-cyclic heptadiagonal matrices. The algorithms are mainly based on the work presented in [A. A. KARAWIA, A New Algorithm for Inverting General Cyclic Heptadiagonal Matrices Recursively, arXiv:1011.2306v1 [cs.SC]]. The symbolic algorithms are suited for implementation using Computer Algebra Systems (CAS) such as MATLAB, MAPLE and MATHEMATICA. An illustrative example is given.