Re: The dimension of fixed space of a matrix

On Sun, 26 Aug 2007 04:15:30 -0000, Gvnaena Pura wrote:

Greetings,

I'm wondering if there is an easy way for knowing the dimension of the
fixed subspace of a matrix, when it act on a vector space. Here, by
the fixed subspace, what I mean is the subspace W such that Mx = x for
all x in W where M is the matrix in question. It is also the kernel
of the map (I-M), where I is the identity. (maybe there is a formal
for this, but I don't know). Thanks in advance.

reduce matrix of M-I

there is a way of know if the dimension of ker(M-I) is != 0
{x: Mx=x}!={0} => 1 is eigenvalue of M
so if you prove that M has not an eigenvalue == 1 =>
{x: Mx=x}=={0}
.

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