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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.
Aug
4
accepted Proof that every finite dimensional normed vector space is complete
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revised What exactly is a differential?
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