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 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\$. 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