Talk:Unitary matrix/Archive 1

Archive 1

hermitian adjoint, represented with a dagger

The conjugate transpose is also known as the hermitian adjoint, represented with a dagger. For example:

U^dagger * U = I_n where the carrot represents a superscript and the underscore the subscript. — Preceding unsigned comment added by 128.193.249.173 (talk) 03:38, 14 April 2003 (UTC)

Finite field

Just a thought but could someone add in an explaination of the unitary group when the field is finite? Since the definition of the unitary matrix relies on the conjugate transpose is there an equivalent definition of "conjugate transpose on a finite field"? TooMuchMath 20:20, 13 April 2006 (UTC)

"if" vs. "if and only if"

"Note this condition says that a matrix U is unitary if it has an inverse which is equal to its conjugate transpose U^* \,." Would it be more precise here to use "if and only if" rather than just "if" ? Or maybe call it an alternative definition? Richard Giuly 05:22, 24 October 2006 (UTC)

Replace plus sign with dagger

Could the writer please replace the plus sign with a dagger? --- —Preceding unsigned comment added by 146.232.75.208 (talk) 16:48, 14 September 2007 (UTC)

matrix dimension versus matrix size

I have a question about the phrase:

"where I_n is the identity matrix in n dimensions"

Based on the start of the article it sounds to me like unitary matrices are all 2 dimentional (n x n). Wouldn't it be more correct for the above phrase to be:

"where I_n is the identity matrix of size n"

Scallop7 (talk) 22:01, 18 June 2009 (UTC)

Symbol conventions

This article uses dagger for conjugate transpose, but in conjugate transpose article we use star. Both articles should use the same notation convention. I personally prefer dagger. What are your preferences? Merilius 21:30, 03 March 2008 (UTC)

I prefer $A^{\dagger }$ both from personal use (quantum mechanics) and for the reduced ambiguity, since * means many things in many contexts. I think, though, that as long as each article uses an internally consistent convention and explains the symbology it is not necessary to regularize them. - Eldereft ~(s)talk~ 21:20, 3 March 2008 (UTC)

Still, it might be useful to explain that $A^{\dagger }$ is the same as $A^{\star }$ in the context of the conjugate transpose article, as many people will link here from pages such as that and normal matrix Westquote (talk)

Although Conjugate transpose uses start, hermitian matrix uses dagger. All related pages should use the same notation noting that there are other notation in the world. —Preceding unsigned comment added by 128.135.198.80 (talk) 18:50, 24 February 2010 (UTC)

Examples needed

Could someone put in some examples of sparse and non-sparce matrices that are unitary? Duoduoduo (talk) 16:10, 25 October 2011 (UTC)

incomplete article and misses major points

the article's first paragraph states, "note this condition implies that a matrix is unitary if and only if it has an inverse which is equal to its conjugate transpose". Sorry but most people cannot comprehend such implications and neither do they have the ability to "note". Especially if the reader is not a mathematical expert. The article should HOW "it is unitary if and only if it has an inverse which is equal to its conjugate transpose". Instead of using vague terminology like "note", the author of this article needs to do a decent job in explaining. Many people come to wikipedia to learn, not to find missing pieces of puzzle. its written in a manner that assumes the reader already has a math degree. — Preceding unsigned comment added by 75.145.240.254 (talk) 02:53, 7 April 2012 (UTC)

Unimodular Matrices

Naive question: Both unitary matrices and unimodular matrices have the property |det(U)|=1. Why is there no mention of unitary matrices in the unimodular matrix article and vice versa? I'm curious to know how they're related and under what circumstances matrices can be both unitary and unimodular.

--Error9312 (talk) 20:27, 3 March 2009 (UTC)

A matrix that is both unitary and unimodular is a permutation matrix, with possibly some 1s replaced by -1s. So the two groups have very small intersection.--Roentgenium111 (talk) 20:10, 31 May 2012 (UTC)