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Aug
25
comment What is the value of this sum? $\sum_{r=k}^{\infty} \frac{1}{r^{3/2} e^{\frac{c k}{2 r}}}$
i think you mean sum
Aug
24
comment show how to prove this question about continuous
did you tried something?
Aug
24
comment A complex matrix with real eigenvalues
Let me tell you this has nothing to do with $10$.... you can take any $2\times 2$ or $3\times 3 $ matrix...
Aug
24
comment Artin's Algebra, Exercise 2.4.11. (1st edition)
Yes... it would be sufficient
Aug
23
comment Artin's Algebra, Exercise 2.4.11. (1st edition)
fine.. May be you could have made it simple.. to prove $x^i\rightarrow y^i$ is a homomorphism it is enough to prove $x\rightarrow y$ is a homomorphism... Then you do not have to write that $i,l$ etc....
Aug
23
comment Relation between Borel sigma algebra on $\mathbb{R} $ and Borel sigma algebra on (n,n+1]
how does an element of borel sigma algebra look like?
Aug
23
comment Artin's Algebra, Exercise 2.4.11. (1st edition)
even then i do not see why do you have to write that map... Btw, your conclusion is correct..
Aug
23
comment Artin's Algebra, Exercise 2.4.11. (1st edition)
I did not get why did you consider the map $\mathbb{Z}\rightarrow G$
Aug
23
comment The number of $2\times 2$ complex matrices satisfying $A^{3}=A$
I think you are asking number upto conjugacy...
Aug
22
comment finitely generated ideal and number of generators
I mean to say $I= \langle a,m\rangle$
Aug
22
reviewed Leave Open An isomorphism between two Banach algebras
Aug
22
reviewed Leave Open Linear Algebra Problem (Spans)
Aug
22
comment finitely generated ideal and number of generators
So, as of now, i understand how does this work... I will be glad if you can give some motivation how did you come up with this idea.....
Aug
22
comment finitely generated ideal and number of generators
I think i got it.. for $r=1$ we have $I=\langle a\rangle +I^2$.. Consider $J=\langle a\rangle$... Let $m\in I$ then, $m\in \langle a\rangle +pq$ for some $p,q\in I$ i.e., $m-pq\in \langle a\rangle$ i.e., $m+ \langle a\rangle=(p+ \langle a\rangle)(q+ \langle a\rangle)$ i.e., $I/J=(I/J)^2$... Now, as $I$ is finitely generated then so is $I/J$... then by same argument as that in my question i would get $m\in I/J$ such that $I/J=\langle m+J\rangle$ then, $I= \langle a\rangle+ \langle m\rangle$.. This is the case for any $r$..
Aug
22
comment If $\lim_{n\to\infty} x_{n+1}-\frac12 x_n = 0$ then $x_n\to 0$
Nice question... good attempt...
Aug
22
comment Find the values of 'a' in a $4\times 4$ matrix(A) when the determinant is less than 2012
yes yes it is +4.... It is column 2 row 4
Aug
22
comment Find the values of 'a' in a $4\times 4$ matrix(A) when the determinant is less than 2012
I have done column operations and not row operations... I did something and ended up with last row with three zeros... There may be some computational errors but this is one of the easy ways... -4 came because i am considering minors/cofactors corresponding to 4,2th element...
Aug
22
answered Find the values of 'a' in a $4\times 4$ matrix(A) when the determinant is less than 2012
Aug
22
comment Differentiability of a two variable function $f(x,y)=\dfrac{1}{1+x-y}$
See this math.stackexchange.com/questions/1007709/…