Talk:Hadamard matrix

message: 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)
thread_title: Anon edits

message: *http://arxiv.org/abs/math.CO/0703312
Might be helpful. Melchoir 02:27, 13 March 2007 (UTC)
thread_title:  Hadamard matrices of order 764 exist 

message: Maybe balanced repeated replication deserves its own page? Will Orrick 01:01, 21 May 2007 (UTC)
thread_title:  Balanced repeated replication 

message: Previously:
 H^{\mathrm{T}} H = n I_n \ 
Now:
 H H^{\mathrm{T}} = n I_n \ 
Matrix multiplication is not commutative.
When I tried to calculate  H^{\mathrm{T}} H = n I_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  H H^{\mathrm{T}} = n I_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 = n I_n \  would be true.
Am I correct? :)  —Preceding unsigned comment added by 82.131.55.64 (talk) 16:47, 8 July 2008 (UTC)
thread_title:  Mistake or not? 

message: The determinant should be 2^{k\cdot2^{k-1}}, but as this is just the usual dependence of the determinant of a Hadamard matrix on its size, it probably doesn't merit special mention. Will Orrick (talk) 17:31, 16 January 2009 (UTC)
replies: text: Yup, that's my bad.  Didn't see the bit on determinants above.  Have a good day, Robinh (talk) 20:39, 16 January 2009 (UTC)
thread_title: Determinant of Sylvester matrix

message: It is a common mistake that Williamson type construction is from Williamson.
It is actually from Golomb and two other co-authors of the paper in 1962.
The construction is named after Williamson because Williamson later proved that
such construction can be generalized for many other (possibly, infinitely many) values of n.
Hysong88 (talk) 01:50, 9 September 2009 (UTC)
replies: text: This is not true.  Williamson's construction dates from 1944.  Baumert, Golomb, and Hall cite Williamson's work in their paper.  I will add literature references to the article. Will Orrick (talk) 19:50, 10 September 2009 (UTC)
thread_title:  Williamson type Hadamard matrices 

message: The word "order" in the discussion of circulant Hadamard matrices did refer to the size of the matrices.  The definition of "circulant" being used here is that each row of the matrix is rotated one unit to the right relative to the row above it.  I have updated the article, pointing the the Wikipedia article where "circulant" is defined, and expanding a bit on what is known about the conjecture.  —Preceding unsigned comment added by Will Orrick (talk • contribs) 23:55, 24 October 2009 (UTC)
thread_title:  Circulant Hadamard matrices 

message: Hello. Can anybody add a example image of some rather small Hadamard matrix? Smth. like mathworld.wolfram.com/HadamardMatrix.html
or even better one http://www.math.pitt.edu/~egw1/Hadamard8.jpg  not with '+' and '-', but with black and white squares. `a5b (talk) 23:03, 9 January 2010 (UTC)
thread_title:  images 

message: I have reverted the edit that added transposition to the list of operations under which Hadamard matrices are considered equivalent.  Obviously there are different possible definitions of equivalence, but if transposition is added to the list, then the numbers of equivalence classes listed in the article become wrong.  For example, for 16×16 Hadamard matrices there are five equivalence classes up to row/column negation/permutation, but only four equivalence classes up to row/column negation/permutation and transposition. Will Orrick (talk) 16:17, 5 February 2010 (UTC)
thread_title:  Equivalence and transposition 

message: In the article it says:
"As a result, the smallest order for which no Hadamard matrix is presently known is 668."
''
and it says:
"As of 2008[update], there are 13 integers n less than or equal to 500 for which no Hadamard matrix of order 4n is known.[6] They are: 167, 179, 223, 251, 283, 311, 347, 359, 419, 443, 479, 487, 491."
''
Isnt that a contradiction? --131.234.106.197 (talk) 14:38, 18 January 2011 (UTC)
replies: text: The two statements agree.  The size of a Hadamard matrix must be a multiple of 4 — sizes 1 and 2 being the sole exceptions.  "Order" in the first statement refers to the actual matrix size.  The n in the second statement is a quarter of the matrix size.  One quarter of 668 is 167, which is the first number on the list of orders for which no Hadamard matrix is known.  Perhaps it's worth trying to clarify the article slightly to avoid confusion. Will Orrick (talk) 20:33, 18 January 2011 (UTC)
thread_title:  For which natural numbers is the Hadamard conjecture known? 

message: I've reverted the edit of 6 October 2011 by user 195.176.20.45.  It is not clear that the "post-publication revision" has been refereed or accepted for publication anywhere, which, in my view, means that the claimed result is not yet suitable for inclusion in Wikipedia.  The edit contained the somewhat odd sentence, "The version that appeared mistakenly contained an older version of the manuscript whose Section 3.3 had a flaw."  By my reading, this is suggesting that it is not the original published article that was in error, but rather the form in which it appeared that was a mistake—as though the publisher accidentally printed a rough draft rather than the finished paper.  If true, this would be an extraordinary story, one that should be backed up, at the very least, by a statement from the publisher.  I have checked the website of the Bulletin of the London Mathematical Society; it does not appear to contain a correction or retraction of the article.  On the other hand, the phrase "post-publication revision", which also appears in the comment line of the arxiv posting, suggests a revision made after publication, implying a different sequence of events.  If more information comes to light, I would be in favor of restoring the reverted edits. Will Orrick (talk) 19:12, 6 October 2011 (UTC)
thread_title:  Circulant Hadamard conjecture