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Jun
16
asked Examples for proof of geometric vs. algebraic multiplicity
Jun
15
accepted Raising a square matrix to the k'th power: From real through complex to real again - how does the last step work?
Jun
14
comment Raising a square matrix to the k'th power: From real through complex to real again - how does the last step work?
So this implies $\frac{z^k+\overline{z}^k}{2}={\rm Re}(z^k)$ and $\frac{z^k-\overline{z}^k}{2}=i{\rm Im}(z^k)$, right?
Jun
14
comment Raising a square matrix to the k'th power: From real through complex to real again - how does the last step work?
Thank you, this clarifies quite a bit. The step seems even to hold when k is real - how does this work?
Jun
14
comment Raising a square matrix to the k'th power: From real through complex to real again - how does the last step work?
Thank you anyway. I agree, the last step is the crucial one. Btw: you have an extra "$" in the following line: "We rewrite this as..."
Jun
14
comment Raising a square matrix to the k'th power: From real through complex to real again - how does the last step work?
@mpiktas: Could you please elaborate - thank you!
Jun
14
revised Raising a square matrix to the k'th power: From real through complex to real again - how does the last step work?
added 118 characters in body; added 15 characters in body
Jun
14
asked Raising a square matrix to the k'th power: From real through complex to real again - how does the last step work?
Jun
10
accepted Function for concatenated semicircles
Jun
10
accepted Question about direct sum of function space
Jun
9
revised Question about direct sum of function space
added 233 characters in body; deleted 6 characters in body
Jun
9
comment Question about direct sum of function space
I think what confuses me is that we start with $\mathbb R^3$ and end up with it. It would come more natural if we started with $\mathbb R$ and after taking the direct sum three times would end in $\mathbb R^3$.
Jun
9
comment Question about direct sum of function space
I think what confuses me is that we start with $\mathbb R^3$ and end up with it. It would come more natural if we started with $\mathbb R$ and after taking the direct sum three times would end in $\mathbb R^3$.
Jun
9
comment Question about direct sum of function space
@Dactyl: Could you please elaborate? So I don't get it...
Jun
9
asked Question about direct sum of function space
Jun
9
comment Function for concatenated semicircles
WA-plot: wolframalpha.com/input/?i=Plot+%28-1%29^%28Floor%5B%28x%2F2+%2B+0.5%2‌​9%5D%29+Sqrt%5B1+-+%28x+-+2+Floor%5Bx%2F2+%2B+0.5%5D%29^2%5D - How did you find it?
Jun
9
comment Function for concatenated semicircles
I now remember that I stumbled upon this phenomenon when you iterate trig funcs: wolframalpha.com/input/… - perhaps this helps and can be combined with some of the other ideas here?!?
Jun
9
comment Function for concatenated semicircles
@Zev: I don't know how to fix this, but I think it goes into the right direction. Floor func is ok.
Jun
9
comment Function for concatenated semicircles
@jspecter: No, please no piecewise def. @Theo: Infinite sums are ok, I think even necessary for the nearly perpendicular inflection points (=infinite slope).
Jun
9
asked Function for concatenated semicircles