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Example?

[edit]

The current example is:

However, the defining property of a jacket matrix is given by:

These currently don't agree (because of the overall scaling by 1/4). Should the property actually read:

?? Oli Filth(talk|contribs) 19:14, 6 April 2009 (UTC)[reply]

You missed part of the definition. It says:
It does not say:
You need to read the whole sentence. Michael Hardy (talk) 21:15, 7 April 2009 (UTC)[reply]
Maybe I'm being slow, but I'm not sure how that validates the "discrepancy" I think exists above! If I understand the notation:
it's saying that each element of the conjugate transpose is the inverse of the corresponding element of the original matrix. This is clearly not the case in the example. Oli Filth(talk|contribs) 22:32, 7 April 2009 (UTC)[reply]

Definition again

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Right, I see someone's fixed the problem I mentioned above. However, the "different form" also worries me:

According to the first condition, this is a necessary condition, but not a sufficient one. Therefore, the two definitions are not equivalent. Presumably it should also include the fact that the summation should equal n when u=v? Oli Filth(talk|contribs) 12:29, 9 April 2009 (UTC)[reply]

I see someone's now removed the alternative definition from the lead. If that's because it's wrong, it also needs removing from the "Properties" section. Oli Filth(talk|contribs) 09:06, 10 April 2009 (UTC)[reply]
Actually, nevermind! I've just realised that's it's self-evident what the summation is when u = v. (). Oli Filth(talk|contribs) 09:16, 10 April 2009 (UTC)[reply]

Actually, no, hang on. That alternative definition is dangerous. Is there anything to prevent these matrices having zero-valued elements? If not, then the alternative definition will be meaningless. Oli Filth(talk|contribs) 09:31, 10 April 2009 (UTC)[reply]

Fields

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Does the jacket matrix work over fields in general, or only over the specific examples mentioned? If it's the former, all that need be said is:

"whose entries are non-zero and from a field."

If it's the latter, it should say:

"whose entries are from a real field, a complex field or a finite field."

Oli Filth(talk|contribs) 10:30, 11 April 2009 (UTC)[reply]

Constraints for orthogonal and unitary matrices

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In the articles for Orthogonal matrix and Unitary matrix, the conditions are clearly stated as and , respectively. In other words, the column vectors form an orthonormal basis, hence:

and

This definition tallies with several sources (e.g. [1], [2], [3], [4], [5]). Now, perhaps their are alternative definitions of orthogonal and unitary matrices out there, but for internal consistency, the definitions on this page need to match those elsewhere in Wikipedia. Oli Filth(talk|contribs) 10:55, 12 April 2009 (UTC)[reply]

A possible compromise is to simply remove the definitions. What purpose do they serve on a page about jacket matrices? Oli Filth(talk|contribs) 01:38, 13 April 2009 (UTC)[reply]

Vandermonde matrix?

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How is the jacket matrix a Vandermonde matrix? The example currently in this article certainly isn't one! Oli Filth(talk|contribs) 12:00, 16 May 2009 (UTC)[reply]

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