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Bounds for the zeros of Bicomplex Polynomials using matrix method

Ovaisa Jan, Idrees Qasim

Abstract

In this paper we investigate bounds for the zeros of a bicomplex polynomial using matrix method. In particular, we find analogue of Gershgorin disk theorem, Cauchy Theorem, theorem of Fujiwara, Walsh and other theorems concerning to zeros of a polynomial to bicomplex polynomials.

Bounds for the zeros of Bicomplex Polynomials using matrix method

Abstract

In this paper we investigate bounds for the zeros of a bicomplex polynomial using matrix method. In particular, we find analogue of Gershgorin disk theorem, Cauchy Theorem, theorem of Fujiwara, Walsh and other theorems concerning to zeros of a polynomial to bicomplex polynomials.
Paper Structure (11 sections, 71 equations)

This paper contains 11 sections, 71 equations.

Table of Contents

  1. Introduction
  2. Preliminary Knowledge
  3. Idempotent elements:
  4. Norm of a bicomplex number:
  5. Bicomplex Matrix:
  6. Eigenvalues and eigenvectors of a bicomplex matrix:
  7. Determinant:
  8. Bicomplex Polynomial:
  9. Companion Matrix:
  10. Main Results
  11. Declaration

Theorems & Definitions (10)

  • proof
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