The Structure and Distribution of Roots of 2×2 Matrices

Yuan Yuan Li

doi:10.4028/www.scientific.net/AMR.765-767.667

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 765-767The Structure and Distribution of Roots of 2×2...

The Structure and Distribution of Roots of 2×2 Matrices

Abstract:

This paper is concerned with Jordan canonical form theorem of algebraic formulae giving all the solutions of the matrix equation X^m= A where n is a positive integer greater than 2 and A is a 2 × 2 matrix with real or complex elements. If A is a 2 × 2 non-singular matrix, the equation X^m = A has infinitely many solutions and we obtain explicit formulae giving all the solutions. If A is a 2 × 2 singular matrix, and we obtained necessary and sufficient condition of square root . This leads to very simple formulae for all the solutions when A is either a singular matrix or a non-singular matrix with two coincident eigenvalues. We also determine the precise number of solutions in various cases.

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Periodical:

Advanced Materials Research (Volumes 765-767)

Pages:

667-669

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.765-767.667

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Online since:

September 2013

Authors:

Yuan Yuan Li

Keywords:

Jordan Canonical Form, Matrix Function, m-th Roots, Non-Singular Matrices, Singular Matrices

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