Re: Pascal Triangle/binomial numbers

I got the solution, I think, using a Cholesky decomposition.

"Bill" <Bill_NOSPAM@xxxxxxxxxxx> wrote in message
news:75KdnfIv2-yk3cfanZ2dnUVZ_qelnZ2d@xxxxxxxxxxxxxx

From the "upper diamond" of Pascal's Triangle ("tilt your head 45
degrees", if necessary), construct the square matrices:

A_1 = { [1] },

A_2 = { [1, 1], [1, 2] },

A_3 = { [1, 1, 1], [1, 2, 3], [1, 3, 6] },

etc.

I am trying to show that each of these matrices A_n, n = 1, 2, 3, ...
are positive semi-definite. Calculations suggest that they are. I would
appreciate any suggestions or references that may be of help. I am hoping
that if I look at things the right way, that it will be obvious.

Thanks,
Bill



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