LaTeX and WordPress (in the wild)
Apparently, you can use LaTeX in wordpress. Alright, he is a practice problem I was working on for my exam in two weeks.
Let with
where
is a
identity matrix and
is a
matrix of ones. Find the eigenvalues of
.
We seek such that
where
is the determinant of a matrix
Now this is merely the equation for determining the eigenvalues of . Since,
is idempotent the eigenvalues of
must be either zero or one. In fact, since this matrix has rank one,
has eigenvalues one with multiplicity one and zero with multiplicity
. Therefore the eigenvalues of
can be found by setting
and
. This yields
with multiplicity
and
with multiplicity
which are exactly the eigenvalues of
.
Cheers.
Posted on February 9, 2010, in Uncategorized. Bookmark the permalink. 1 Comment.
This article was very useful for a paper I am writing for my thesis.
Thanks
Bernice Franklin
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