- #1

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[itex] \begin{pmatrix} 2x & 0 \\ 0 & 2y \end{pmatrix} [/itex]

so surely by the Cauchy–Riemann equations this is complex differentiable at [itex] x = y [/itex], but is this function holomorphic anywhere?

Thanks!

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- Thread starter blahblah8724
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- #1

- 32

- 0

[itex] \begin{pmatrix} 2x & 0 \\ 0 & 2y \end{pmatrix} [/itex]

so surely by the Cauchy–Riemann equations this is complex differentiable at [itex] x = y [/itex], but is this function holomorphic anywhere?

Thanks!

- #2

HallsofIvy

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By the way, the phrase "holomorphic anywhere" does not make sense. "Holomorphic" means "analytic for all complex numbers". You mean to ask if it was analytic anywhere.

- #3

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? According to the Wikipedia article, holomorphic at a point means complex-differentiable in some neighborhood of the point. So asking whether a function is holomorphic anywhere does make sense.By the way, the phrase "holomorphic anywhere" does not make sense. "Holomorphic" means "analytic for all complex numbers". You mean to ask if it was analytic anywhere.

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