Re: Calculating a generalized inverse matrix

On Nov 13, 10:21 am, Allen McIntosh <nos...@xxxxxxxxxxxxxxxx> wrote:
Gary wrote:
On Nov 12, 9:25 am, Ying-Foon Chow <yfchow.c...@xxxxxxxxx> wrote:
I'd appreciate if someone can tell me if I could find a (generalized)
inverse matrix of a singular matrix using Excel. Specifically, I have
a square matrix, say 10 by 10, but I know the rank of the matrix is 8.
Still, I need to find its "inverse" in order to construct a statistic.
I must be missing something. why not just use MINVERSE?
see http://www.stanford.edu/~wfsharpe/mia/mat/mia_mat4.htm

As the OP says, the matrix is 10x10 but only has rank 8. The Stanford
web page says specifically that MINVERSE() requires an "invertible"
(i.e. non-singular) matrix.

Paige Miller's advice is probably best, but if that's not possible then
ask if you really need to compute the inverse explicitly. If all you
are going to use it to compute a couple of matrix-vector products, you
can often find a way to compute those without computing the
(generalized) inverse first.

Thank you for your responses. The task I am trying to is to compute a
statistic which is a quadratic form: a'*S^{-1}*a where a is 10 by 1
vector and S is 10 by 10 (covariance) matrix. As can be seen, I need
the inverse of S, but the problem is I know S is singular. May I know
if there is any solution to this problem in statistics literature?

Indeed, this problem is much easier in other matrix programming
languages mentioned in Paige Miller's post, but I just thought Excel
is easier for demonstration purpose. By the way, the "brute force"
method that I was told elsewhere is to get add-ins that can do
singular value decomposition, and I think I can get the pointers by
searching Google.

Thanks and regards,
Y. F.

.

Relevant Pages

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