Talk:Hadamard matrix

hadamard configuration

Anon edits

Hadi Kharaghani and Behruz Tayfeh-Rezaie announced on 21 June 2004 that they constructed a Hadamard matrix of order 428. As a result, the smallest order for which no Hadamard matrix is presently known is 668.

Anon, would you please advise us what your objection is to this statement? Bearcat 03:49, 7 September 2006 (UTC)[reply]

You can actually download a text file of their matrix and verify it yourself, so what's the problem? Ntsimp 17:11, 12 September 2006 (UTC)[reply]

Hadamard matrices of order 764 exist

http://arxiv.org/abs/math.CO/0703312

Might be helpful. Melchoir 02:27, 13 March 2007 (UTC)[reply]

Balanced repeated replication

Maybe balanced repeated replication deserves its own page? Will Orrick 01:01, 21 May 2007 (UTC)[reply]

Mistake or not?

Previously: $H^{\mathrm {T} }H=nI_{n}\$

Now: $HH^{\mathrm {T} }=nI_{n}\$

Matrix multiplication is not commutative.

When I tried to calculate $H^{\mathrm {T} }H=nI_{n}\$ , the result did not derive from the definition: I am to multiply items from columns of matrix H when rows (not columns) of matrix H are supposed to be orthogonal.

When one tries to calculate $HH^{\mathrm {T} }=nI_{n}\$ , everything comes out logically. (IMHO: I could have been mistaken).

This page Mathworld page has it also in the same way.

But, if the definition would be given as follows: "In mathematics, a Hadamard matrix is a square matrix whose entries are either +1 or −1 and whose columns are mutually orthogonal.", then the following formula $H^{\mathrm {T} }H=nI_{n}\$ would be true.

Am I correct? :) —Preceding unsigned comment added by 82.131.55.64 (talk) 16:47, 8 July 2008 (UTC)[reply]

Actually both are true, but I agree that the way you have it now, $HH^{\mathrm {T} }=nI_{n}\$ does follow more directly from the definition as stated. The way it was previously follows from the fact that $H^{\mathrm {T} }=nH^{-1}\$ and therefore commutes with $H$ . This, of course, is not quite as immmediate. Will Orrick (talk) 19:34, 8 July 2008 (UTC)[reply]

Plain English

One of the things I hate about mathematical notation (especially in an Encyclopedia!) is that the definitions of the notations used are not immediately obvious to someone who's forgotten their math (or never learned it) and doesn't have an easily readable notation cheat sheet on hand.

From context, I'm assuming $HH^{\mathrm {T} }=nI_{n}\$ (thanks to the person above for the math markup) means "The matrix H noncommutatively multiplied with the matrix H to the Tth power (where the variable[?] T isn't defined) is equal to n times the nxn identity matrix. Is this correct? What does $\operatorname {det}$ mean?

Could those who write these articles begin appending plain (mathematical) language descriptions for those who haven't used matrix algebra (or whatever) in the previous decade (or ever)? I'd greatly appreciate it, I'm sure others would as well. --99.14.107.65 (talk) 05:04, 27 October 2008 (UTC)[reply]