Talk:Transpose

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How about the alternative notation of A' for a transposition of A? Chris Wood 20:11, 9 Mar 2004 (UTC)

Another note -- should mention that the generalization of the notion of transpose to complex matrices is to make element (i,j) equal to the conjugate of the (j,i) element. I agree with Chris W that the notation A' should be mentioned as an alternative. Wile E. Heresiarch 08:39, 11 Mar 2004 (UTC)

1 Differentiation of transposed matrices
2 Transpose of linear maps
3 hermitian transpose?
4 Transpose in Music area
5 yes.

[edit] Differentiation of transposed matrices

I was trying to understand what the derivative of a transposed matrix is with respect to that matrix? So something like $\frac{\mathrm{d}A \Theta}{\mathrm{d}\Theta}$ where both are matrices.
yanneman 13:26, 20 November 2006 (UTC)

[edit] Transpose of linear maps

In the Transpose of linear maps section, the article had read:

If f : V→W is a linear map between vector spaces V and W with dual spaces W* and V*, we define the transpose of f to be the linear map ^tf : W*→V* with

${}^t f (\phi) = \phi\circ f\,$

for every $\ \phi$ in W*.

An anonymous user changed that to

If f : V→W is a linear map between vector spaces V and W with dual spaces W* and V*, we define the transpose of f to be the linear map f^T : W*→V* with

$f (\phi)^{\mathrm{T}} = \phi\circ f\,$

for every $\ \phi$ in W*.

Now, I think that's confusing (it's f that's transposed, not f(φ)), and it would be better to write

$f^{\mathrm{T}}(\phi) = \phi\circ f\,$

for every $\ \phi$ in W*.

But even that seems ambiguous; is this "transpose f" or "f to the T power"? But I'm unfamiliar with this notation, and I certainly don't have the same objection to ^T used with matrices. So, are there any experts who could weigh in with the most common usage in this area? (I'm not proposing to change the ^T notation used in the earlier sections, just to keep the ^t notation in this one section.) --Quuxplusone 21:14, 8 August 2005 (UTC)

[edit] hermitian transpose?

hermitian transpose = conjugate transpose? --Moala 09:23, 20 December 2005 (UTC)

[edit] Transpose in Music area

Often, Transpose in Music area refers to Pitch(Music). But is there any algorithm to set that?

[edit] yes.

yes, there is

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Talk:Transpose

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[edit] Differentiation of transposed matrices

[edit] Transpose of linear maps

[edit] hermitian transpose?

[edit] Transpose in Music area

[edit] yes.

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