Some properties of n x n generalized idempotent matrices with entries 1 and -1 satisfying m2 = m m (1 ≤ m ≤ n)
International Journal of Development Research
Some properties of n x n generalized idempotent matrices with entries 1 and -1 satisfying m2 = m m (1 ≤ m ≤ n)
Received 27th August 2017; Received in revised form 19th September, 2017; Accepted 18th October, 2017; Published online 30th November, 2017
Copyright ©2017, Dr. Bakshi Om Prakash Sinha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper n x n generalized idempotent matrix M is defined with entries 1, -1 satisfying M2 = mM (1 ≤ m ≤ n) with examples. It is a quite new concept. We have discussed its properties that the Kronecker product of two generalized idempotent matrices is also a generalized idempotent matrix. Also if a n x n matrices M with entries 1 and -1 satisfies M2 = m M ( 1 ≤ m ≤ n ) then the column of matrix M are eigen vector corresponding to eigen values of M.
