%0 Journal Article
%T Two Eigenvector Theorems
%A Raghuram Prasad Dasaradhi
%A V. V. Haragopal
%J Advances in Linear Algebra & Matrix Theory
%P 11-16
%@ 2165-3348
%D 2016
%I Scientific Research Publishing
%R 10.4236/alamt.2016.61002
%X In this
paper, we established a connection between a square matrix ¡°<i>A</i>¡± of order ¡°n¡± and a matrix <img src=\"Edit_a8fa582f-8a93-46df-a8ce-f457dc9f7598.bmp\" alt=\"\" /><span lang=\"EN-US\">&nbsp;defined through a new approach of the
recursion relation&nbsp;<img src=\"Edit_6c6d1d63-f1b9-406f-a194-029105f2738f.bmp\" alt=\"\" />. (where <img src=\"Edit_7c0f89a5-302c-4e74-b12a-b1e1231cd9bf.bmp\" alt=\"\" />&nbsp;is any column matrix with n real elements).
Now the new matrix <img src=\"Edit_bee5279a-a78e-4be5-8823-e0dab2e8fc92.bmp\" alt=\"\" />&nbsp;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.</span>
%K Characteristic Equation
%K Minimal Polynomial
%K Eigenvalues
%K Eigenvectors
%K Vander Monde Matrix
%K Jacobi Block Matrix
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=64299