Here is a way:

sage: m = Matrix(CDF, 2,2, [1,2*I,3-I,-4])
sage: m

[        1.0       2.0*I]
[3.0 - 1.0*I        -4.0]
sage: m.transpose()

[        1.0 3.0 - 1.0*I]
[      2.0*I        -4.0]
sage: m.transpose().list()
[1.0, 3.0 - 1.0*I, 2.0*I, -4.0]
sage: mstar = Matrix(CDF, 2,2, [x.conjugate() for x in m.transpose().list()])
sage: mstar

[        1.0 3.0 + 1.0*I]
[     -2.0*I        -4.0]


There might be something simpler though.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++

On 5/22/07, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote:
>
> Greetings,
>
> After a cursory look through the documents, I could not see any
> obvious method for computing a conjugate or Hermitian transpose on a
> matrix in the complex double field. I have gotten only this far:
>
> sage: m = Matrix(CDF, [[1,2*I],[3-I,-4]])
> sage: m
> [        1.0       2.0*I]
> [3.0 - 1.0*I        -4.0]
> sage: m.transpose()
> [        1.0 3.0 - 1.0*I]
> [      2.0*I        -4.0]
> sage: (3*-I).conjugate()
> 3.00000000000000*I
>
> Conjugate isn't defined for matrices, so I presume I should apply it
> element wise ...
>
> I am really enjoying experimenting with sage. Thanks for the hard work
> put into it,
>
> -carson-
>
>
> >
>

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