Two Eigenvector Theorems - Advances in Linear Algebra & Matrix Theory

ALAMT > Vol.6 No.1, March 2016

Two Eigenvector Theorems ()

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DOI: 10.4236/alamt.2016.61002 3,131 Downloads 4,680 Views

Author(s)

Raghuram Prasad Dasaradhi^1*, V. V. Haragopal²

Affiliation(s)

¹Department of Mathematics, Osmania University, Hyderabad, India.
²Department of Statistics, Osmania University, Hyderabad, India.

ABSTRACT

In this paper, we established a connection between a square matrix “A” of order “n” and a matrix

defined through a new approach of the recursion relation

. (where

is any column matrix with n real elements). Now the new matrix

gives us a characteristic equation of matrix A and we can find the exact determination of Eigenvalues and its Eigenvectors of the matrix A. This new approach was invented by using Two eigenvector theorems along with some examples. In the subsequent paper we apply this approach by considering some examples on this invention.

KEYWORDS

Characteristic Equation, Minimal Polynomial, Eigenvalues, Eigenvectors, Vander Monde Matrix, Jacobi Block Matrix

Share and Cite:

Dasaradhi, R. and Haragopal, V. (2016) Two Eigenvector Theorems. Advances in Linear Algebra & Matrix Theory, 6, 11-16. doi: 10.4236/alamt.2016.61002.

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