# [SciPy-user] Structured matrices

Anand Patil anand@soe.ucsc....
Wed Mar 14 11:06:58 CDT 2007

Nils, Barry,

That matrix is also the covariance of Brownian motion evaluated at times [9, 7, 5, 3, 1]. The inverse matrix bears a strong resemblance to the numerical second derivative operator. This makes sense because the second derivative in x of min(x, \xi) is a delta function concentrated at \xi, but there's probably a more important connection that I don't know about.

Maybe this helps explain the strange results? I found some related refs, but haven't looked at them: http://citeseer.ist.psu.edu/347057.html, http://adsabs.harvard.edu/abs/2003EAEJA.....2001X .

Cheers,
Anand

--------------------------

Nils,
Does this matrix come from a particular application?  I'm working on algorithms for the non-negative matrix factorization (NMF).  With this matrix as input I'm getting some very strange results.  So I'm curious about potential applications.

Cheers!
Barry L. Drake
GA Tech

Nils Wagner wrote: Hi all,

I was wondering if the matrix family (see below) has a special name ?
And/or is there a way to construct this matrix via special matrices
(like Hankel, Toeplitz, etc.) ?

[[ 3.  1.]
[ 1.  1.]]

[[ 5.  3.  1.]
[ 3.  3.  1.]
[ 1.  1.  1.]]

[[ 7.  5.  3.  1.]
[ 5.  5.  3.  1.]
[ 3.  3.  3.  1.]
[ 1.  1.  1.  1.]]

[[ 9.  7.  5.  3.  1.]
[ 7.  7.  5.  3.  1.]
[ 5.  5.  5.  3.  1.]
[ 3.  3.  3.  3.  1.]
[ 1.  1.  1.  1.  1.]]

Nils