Re: A simple problem in linear algebra

On 27.08.2007 21:13, Gvnaena Pura wrote:

Let M be a n-by-n permutation matrix, let x be a n-vector, such that
Mx /= x, and m = n - dim(Ker(I-M)). Now I want to either prove of
refute the statement that {x, Mx, (M^2)x, ..., (M^m)x} are AFFINELY
independent.

PS: n - dim(Ker(I-M)) is the dimension of the orthogonal space of the
fixed subspace of M.

Did you try the 3x3-matrix M over the reals corresponding to the transposition (1,2) with a very special choice of x?
.

Relevant Pages
Quantcast