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Feb
1
revised If I know that a matrix $G = (X^{T}X)^{-1}$, how can I recover what $X$ is?
added 266 characters in body
Feb
1
answered If I know that a matrix $G = (X^{T}X)^{-1}$, how can I recover what $X$ is?
Jan
30
answered What does y=y(x) mean?
Jan
30
answered If $\{x_n\}$ satisfies that $x_{n+1} - x_n$ goes to $0$, is $\{x_n\}$ a Cauchy sequence?
Jan
14
comment Solution to Sextic Polynomial with Two Real Roots
The only helpful thing I can see is that the polynomial can be written as $3a(x^{2}-1)^{3}+6x^{5}-4x^{3}+6x$. I can't see how to take this any further, though (and I'm sure you'd have noticed if one of your roots was always $\pm1$).
Jan
14
answered How to find the maximum of this function $\frac{x}{x-y}$?
Jan
13
comment How to show that for all $a \in \mathbb{C}$ there is a unique $b \in \mathbb{C}$ such that $ab = 1$?
Or, rather, the proof is the very short "By axiom IV, done" or something
Jan
13
comment How to show that for all $a \in \mathbb{C}$ there is a unique $b \in \mathbb{C}$ such that $ab = 1$?
@Lsonic Are you sure those axioms weren't given for $\mathbb{R}$ instead? As the other commenters note, the statement you are trying to prove in your question is true if and only if elements of $\mathbb{C}$ have multiplicative inverses. If that is one of your axioms, then you can't prove your statement because it is axiomatically true.
Jan
13
answered Every open set in $\mathbb{R}$ is a disjoint union of open intervals: I'm struggling to follow the disjoint constraint
Jan
13
comment Size of Jordan blocks
Regarding "which block comes first on the diagonal?", Jordan normal form is unique up to permuting the blocks. That is, it doesn't matter which comes first.
Jan
13
answered How to show that for all $a \in \mathbb{C}$ there is a unique $b \in \mathbb{C}$ such that $ab = 1$?
Dec
31
answered Impossible events that actually happened
Dec
23
comment Matrix inverse series expansion
Fair enough, thanks!
Dec
23
comment Matrix inverse series expansion
Unless you mean the fact that the set of $K$ such that $I+K$ is invertible is dense in the set of $n\times n$ matrices (and hence the limit exists), is that it?
Dec
23
comment Matrix inverse series expansion
@G. Sassatelli Fair point, I've edited it to something hopefully more sensible. I did indeed mean that the matrix should have small norm - why does that make the invertibility condition superfluous?
Dec
23
revised Matrix inverse series expansion
deleted 38 characters in body
Dec
23
asked Matrix inverse series expansion
Dec
20
comment cardinality of the set $\{z\in \Bbb C : z^{98} =1\; and \;z^n\neq1 \;for\; any\; 0\lt n\lt98 \;\}$
I'm not sure exactly what you mean by "I was thinking about $98^{th}$ roots of unity" - this is a set which contains them; is that what you mean?
Dec
13
comment $A$ be a subset of $[0,1]$ with non-empty interior ; then is it true that $\mathbb Q+A=\mathbb R$?
What if $A=(1/3,2/3)$?
Dec
1
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