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Aug
9
comment Are all matrices linear operators?
I will think about this some time. For now I do understand what you meant in your previous comment but I still don't see why a matrix does not define a linear map.
Aug
9
comment Are all matrices linear operators?
Honestly, I really really don't understand how a matrix is a map $\{1,\dots,m\}\times\{1,\dots,n\} \to \mathbb{K}$. It seems to me that it takes vectors of arbitrary real numbers as argument not just integer pairs in these finite sets...?
Aug
9
comment Are all matrices linear operators?
An $n \times m$ matrix with real entries is a map $\mathbb R^m \to \mathbb R^n$. So please do continue.
Aug
9
comment Are all matrices linear operators?
Alright. Can you humour me and point out to me which of the parts of the definition of a linear map a matrix does not satisfy?
Aug
9
comment How do I find a root of $A^2$?
Yes! Exactly! : )
Aug
9
comment Are all matrices linear operators?
Sorry, does your first sentence really say that matrices do not satisfy the definition of a linear map?
Aug
9
comment Are all matrices linear operators?
Yes. ${}{}{}{}{}$
Aug
9
comment How do I find a root of $A^2$?
The first thing that came to my mind when I read your question was "Hm... can I diagonalise $A$ and then take the root of $D$?"
Aug
9
comment Find matrix representing Linear Transformation
As far as I can tell you are not "given the correspondence between the two (0,0)" either. Hence I would assume that the vertices are mapped in order.
May
8
comment Express unit sphere as countable union of great circles?
@Misakov The version I state is equivalent to yours if you replace union with intersection (see e.g. here. In your other comment, if you replace dense with open dense in the conclusion then yes, it seems to me that you can argue like that.
May
8
comment Express unit sphere as countable union of great circles?
@Misakov I elaborated on this hint. Maybe it helps you answer your comment here.
Apr
27
comment $p$-adic completion of integers
@user135520 Which sequence are you talking about? It's quite some time since I wrote this post...
Mar
7
comment Intersection of all neighborhoods of zero is a subgroup
@TobiasKildetoft Thank you for your comment!
Feb
20
comment Are these linear maps bounded?
Seriously: first you pretend you can solve the exercise by "giving" "overgenerous hints" and when I press you for an answer you admit you can't solve it either.
Feb
20
comment Are these linear maps bounded?
I think is clear that the idea of the exercise is to give an explicit example.
Feb
20
comment Are these linear maps bounded?
What's an example of an oscillating function with compact support?
Feb
20
comment Are these linear maps bounded?
Yes, I would like to see an example of a sequence of $f_n$ with $\|f_n\|_\infty \le 1$ and $\|f_n'\|_\infty$ unbounded. Because that's what I've been trying to construct for the past 30 minutes but have not managed. I believe this is what's difficult about this exercise.
Feb
19
comment Are these linear maps bounded?
I also rolled back an entirely unnecessary edit.
Feb
19
comment Are these linear maps bounded?
I upvote in order to compensate for the spite downvote.
Feb
14
comment Hilbert space structure on $C^{*}$ algebras
@JonasMeyer Interesting. Please could you elaborate on your comment?