n TH POWER (n IS A REAL NUMBER) OF A SQUARE MATRIX BY USING DIAGONALIZATION METHOD,APPLICATIONS OF DIAGONALIZATION.

Authors: M.RAJESH

Country: India

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Abstract: The aim of the present paper is to find the nth root of a square matrix by the process of diagonalization. We can find the nth root of a square matrix if it is diagonalizable. A diagonal matrix is a square matrix whose elements other than the principal diagonal are zero. A square matrix is said to be diagonalizable if there exists an invertible square matrix P such that
A=PDP-1 or AP=PD, where D is a Diagonal matrix. The process of diagonalizing a matrix is defined as diagonalization. For the process of diagonalizing a matrix, we have to find eigen values, eigen vectors of the matrix.

Keywords: Key words: Square matrix, Diagonal matrix, Eigen values, Eigen vectors.

Paper Id: 231310

Published On: 2024-10-10

Published In: Volume 12, Issue 5, September-October 2024

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