2,668 reputation
2236
bio website ephorie.de
location Germany
age 44
visits member for 4 years, 4 months
seen 2 days ago

just an amateur fascinated by math


Jun
17
accepted Examples for proof of geometric vs. algebraic multiplicity
Jun
17
answered I was wondering what is the simplest yet difficult mathematical question?
Jun
17
comment Examples for proof of geometric vs. algebraic multiplicity
Thank you so much - awesome!
Jun
16
comment Examples for proof of geometric vs. algebraic multiplicity
That would be super - thank you in advance!
Jun
16
comment Examples for proof of geometric vs. algebraic multiplicity
@Javier: Thank you very much for your extensive answer! I don't know if it is an impolite request to ask you too for an example like the one Mariano gave (but here of course with the reasoning of the proof?) Especially how they extend the set to a basis of V and the resulting matrix M is not clear to me and I think an example would be extremely helpful for understanding the reasoning. In any case: Thank you again!
Jun
16
comment Examples for proof of geometric vs. algebraic multiplicity
I see, anyway: examples are always good to exemplify the theory (at least I desperately need them!) - perhaps you could extend your answer? Thank you in any case!
Jun
16
comment Examples for proof of geometric vs. algebraic multiplicity
Thank you. Unfortunately you don't give any examples that connect to the proof as I asked. Perhaps you can add some? Thank you again!
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 $\mathbb R^3$.