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Sep
15
accepted Questions on proof that for $U$-invariant diagonalisable maps, the restriction $A_{|U}$ is diagonalisable too
Sep
15
comment Questions on proof that for $U$-invariant diagonalisable maps, the restriction $A_{|U}$ is diagonalisable too
Okay, guess now I got the point. But in the first argument I think $u \in U\setminus U_1$ is choosen such that in its linear combination a minimal number of eigenvectors is involved, so that every element with less eigenvectors in any linear combination is contained in $U_1$, right?
Sep
15
asked Questions on proof that for $U$-invariant diagonalisable maps, the restriction $A_{|U}$ is diagonalisable too
Sep
12
accepted A seemingly simple fact about construction of maps proven categorically, i.e. by universal properties
Sep
12
comment A seemingly simple fact about construction of maps proven categorically, i.e. by universal properties
Yes, sorry this was unclear, I meant it in the way Hagen von Eitzen answered my question!
Sep
12
revised A seemingly simple fact about construction of maps proven categorically, i.e. by universal properties
added 1 character in body
Sep
12
asked A seemingly simple fact about construction of maps proven categorically, i.e. by universal properties
Sep
12
accepted Decomposing linear mapping between direct sums of vector spaces
Sep
12
comment Decomposing linear mapping between direct sums of vector spaces
Thanks for pointing out, I forgot existence. The map $A$ defined that way is actually linear, for if $u,v$ with $v = v_1 + \ldots v_n$ and $u = u_1 + \ldots + u_n$ we have $A(u+v) = A((u_1+v_1)+\ldots+(u_n+v_n)) = A_1(u_1+v_1) + \ldots + A_n(u_n+v_n) = A_1u_1 + \ldots + A_nu_n + A_1 v_1 + \ldots + A_n v_n$, where commutativity and linearity of the $A_i$'s was used in the rearrangements. The fact that $A(\lambda v) = \lambda A(v)$ is shown similar.
Sep
12
asked Decomposing linear mapping between direct sums of vector spaces
Sep
12
accepted About a Property of maximal solutions of separable ODE's $y'=g(x)h(y)$ for locally Lipschitz $h : U\to\mathbb R$, $U$ open
Sep
12
accepted Show that for commuting projections we have $\mbox{im}(PQ) = \mbox{im}(P) \cap \mbox{im}(Q)$
Sep
11
asked Show that for commuting projections we have $\mbox{im}(PQ) = \mbox{im}(P) \cap \mbox{im}(Q)$
Sep
6
asked Show that certain sequence used in the proof of Wallis product formula is decreasing
Sep
5
accepted Why such a complicated counterexample to differentiable function, which has discontinuous partial derivatives
Sep
5
comment Why such a complicated counterexample to differentiable function, which has discontinuous partial derivatives
@HaraldHanche-Olsen: Nice, found it under the name Darboux's Theorem, en.wikipedia.org/wiki/Darboux's_theorem_(analysis) ;)
Sep
4
comment Why such a complicated counterexample to differentiable function, which has discontinuous partial derivatives
yes, that it... completely overlooked o_O
Sep
4
asked Why such a complicated counterexample to differentiable function, which has discontinuous partial derivatives
Sep
1
comment Question on a derivation regarding the non-linear ODE $x'' = -U'(x)$, $U$ potential
by chain rule: $f'(f^{*}(x))\cdot (f^{*}(x))' = 1$, and therefore $(f^{*}(x))' = 1 / f'(f^{*}(x))$. In terms of differentials, if $dy/dx = g(x)$, then $dx/dy = 1/g(x) = 1/g(x(y))$, expressed in terms of $y$.
Aug
31
revised About a Property of maximal solutions of separable ODE's $y'=g(x)h(y)$ for locally Lipschitz $h : U\to\mathbb R$, $U$ open
edited tags