Dear Devon and others:
I'm quite profficient in the standard linear algebra with linear and
quadratic forms of random vectors. So the variance of an (m x 1) random
vector x is an (m x m) matrix whose ijth element is cov(x[i], x[j]), and
Var(Ax) = A Var(x) T(A).
But I'd like to take the variance of an (m x n) random matrix X. This would
be an (m x n x m x n) array (or better, an ((m x n) x (m x n)) matrix) whose
(ij)(kl)th element is cov(x[ij], x[kl]). And I'd like also to generalize
that quardratic form.
So I'm seeking to generalize matrices from {linear mappings from n-space to
m-space} to {linear mappings from (n1 X n2)-space to (m1 x m2)-space}. At
the very least, I can ravel (,) the axes and do it as (m1*m2) x (n1*n2)
matrices. But I wonder if something more powerful exists.
Sincerely,
Leigh
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Devon McCormick
Sent: Monday, February 22, 2010 10:56 AM
To: Programming forum
Subject: Re: [Jprogramming] Generalized Matrix Multiplication
I see my comment about conformability was too specific to matrix
multiplication. I see from Roger's comment that we should consider the more
general case for what constitutes conformability. I'll have to think of a
more practical example, but here's one for conformability that does not
require the inner dimensions to match:
(i.3 4) +/ . ,/ i.5 5
62 70 78 86 70
On Mon, Feb 22, 2010 at 10:42 AM, Roger Hui <[email protected]> wrote:
> ...
> For general u . v the conformability requirements depend
> on the left rank of v and the shape of the result depend
> on the shapes of results produced by u and v , as
> the definition u . v <-> u@(v"(1+lv,_)) would indicate.
> ...
>
--
Devon McCormick, CFA
^me^ at acm.
org is my
preferred e-mail
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