1,707 reputation
612
bio website cse.iitb.ac.in/~aruniyer
location India
age 31
visits member for 2 years, 8 months
seen 8 hours ago

2d
awarded  Constituent
Dec
8
awarded  Caucus
Dec
6
answered How to prove that $A^2$ is a symmetric matrix
Dec
2
comment Computing eigenvector corresponding to dominant eigenvector.
en.wikipedia.org/wiki/Power_iteration
Nov
26
comment How to prove $n < \left(1+\frac{1}{\sqrt{n}}\right)^n$
You can lower that limit of 144 even further. Note that $$ 1 + \sqrt{n} + \dfrac{(n-1)}2 + \dfrac{n(n-1)(n-2)}{6} \dfrac1{n^{3/2}} = \frac{n^{3/2}}{6} + \frac{n}{2} + \frac{n^{1/2}}{2} + \frac{1}{3n^{1/2}} + \frac{1}{2}$$. The RHS is greater than (using the first three terms) $$\frac{n}{2} + \frac{n^{1/2}(n + 3)}{6}$$. It is quite easy to show that $$\frac{n^{1/2}(n + 3)}{6} > \frac{n}{2}$$. This gives you the result, without needing calculus or computing for particular values.
Nov
25
answered Efficient inversion of a symmetric, positive definite matrix
Nov
19
answered Prove $ A^-=\dfrac{1}{4}(-A^2+4A+I)$
Nov
19
revised show that $\mathsf E(Y|X)=\mu_2+\rho\dfrac{\sigma_2}{\sigma_1}(X-\mu_1)$
edited body
Nov
19
answered show that $\mathsf E(Y|X)=\mu_2+\rho\dfrac{\sigma_2}{\sigma_1}(X-\mu_1)$
Nov
17
revised Can product of two singular matrices be invertible?
The implications go both ways
Nov
17
suggested approved edit on Can product of two singular matrices be invertible?
Nov
15
comment Jensen’s inequality
@Did Then hopefully the wikipedia link is sufficiently helpful.
Nov
15
revised Jensen’s inequality
edited body
Nov
15
answered Jensen’s inequality
Nov
14
awarded  Civic Duty
Nov
14
comment Eigenvalues of a sum of rank-one matrices?
This is excellent!
Nov
11
answered Why is this nested sum formula true
Nov
8
comment Counterexample for $\| (\Phi^\top \Xi \Phi)^\dagger \Phi^\top \Xi P \Phi \|_2 \leq 1$
Are they no conditions on phi like norm phi <= 1?
Oct
27
revised Prove $\int_0^{2\pi}\frac{3a\sin^2\theta}{(1-a\cos \theta)^4}$ or $\int_0^{2\pi}\frac{\cos\theta}{(1-a\cos\theta)^3}=\frac{3a\pi}{(1-a^2)^{5/2}}$
added 25 characters in body
Oct
27
comment Limit of $n(a^{1/n}-1)$ as $n \to \infty$
You mean $(e^x - 1)/x$. Also as n tends to infinity, x tends to 0.