TenaliRaman

1,146 reputation

310

bio	website	cse.iitb.ac.in/~aruniyer
	location	India
	age	29
visits	member for	1 year
	seen	9 hours ago
stats	profile views	111

	1,146 reputation	bio	website	cse.iitb.ac.in/~aruniyer	visits	member for	1 year
310 badges		location	India		seen	9 hours ago

summary answers questions tags badges favorites bounties reputation activity

118 Comments

suggestions reviews revisions comments badges posts accepts all

Mar 21	comment	norm of a linear operator For a fixed $x$, $\\|A(x)\\| = \\|A(\frac{x}{\\|x\\|})\\| \\|x\\| \leq \\|A\\|\\|x\\|$. The first step uses linearity of the operator and the second step uses definition of the operator norm. This is not a complete proof, one has to consider some case, but the gist of the proof is just this much.
Mar 21	comment	Finding a vector orthogonal to a subspace What is wrong with your finding x such that Ax = 0 idea? I see it as completely correct way of going about this.
Mar 9	comment	Is the set of all straight lines in the plane whose slope and y-intercept are integers countable? If f is a bijective map from N to P, then even $(m, n) \mapsto (f(m), f(n))$ should be bijective from NxN to PxP.
Feb 6	comment	Prove by using Pigeon Hole Principle @chihiroasleaf Said differently, consider the set {3, 33, 333, 3333, ...., (3 repeated k times)}. Now, any number when divided by k can give remainders between 0 and k - 1. Now, divide each number in the given set with k and observer the remainders that they give. What happens if one of the remainders is zero and what happens if none of the remainders are zero?
Jan 27	comment	How variance is defined? What you propose is another way of measuring spread - it is called mean absolute deviation.
Jan 25	comment	Proving Hölder's Inequality You just need Jensen's Inequality. Check out @mike 's comment here - math.stackexchange.com/questions/211633/…
Jan 24	comment	Subspace of a Hilbert Space @Norbert, after reading Martin's answer I see how you made that connection :-) I was going through the link you suggested several times, honestly though I wasn't smart enough to see the similarities :-).
Jan 24	comment	Subspace of a Hilbert Space Thank you! This answer has gone a long way into making me understand several different things! :-)
Jan 24	comment	Subspace of a Hilbert Space @Martin I have added the uniform boundedness principle to the question.
Jan 6	comment	how do you learn trigonometric identities @GiuseppeNegro Wow, that is neat!
Jan 6	comment	how do you learn trigonometric identities @GiuseppeNegro Wow, I did not know that! That is a very interesting piece of info (+1). Thank you!
Jan 6	comment	Minimization to Maximization doubt in SVM You are correct about both, 1] there are constraints that essentially rule x being 0 and 2] the 1/2 is just to make the derivative pretty.
Dec 27	comment	Prove this equation $x$ in this case is $\lambda m + o(m)$.
Dec 27	comment	Prove this equation As $m$ approaches 0, you can write $\log(1 + x)$ in terms of its taylor expansion.
Dec 27	comment	Does linearity decompose down convex sums? If f is linear, then f is convex as well as concave.
Dec 18	comment	Specific inequality Can you please share references for the Dao Hai Long inequality? Thank you :-).
Dec 15	comment	Calculate $\int_0^2 x^2 e^x dx$ If you call LHS as $I(n)$, then $I(n) = 2^ne^2 - nI(n - 1)$, therefore $I(2) = 4e^2 - 2(2e^2 - I(0)) = 4e^2 - 4e^2 + 2I(0) = 2e^2 - 2$ where $I(0)$ is explicitly evaluated.
Dec 6	comment	Show that a function is uniformly continuous Your definition of Lipschitz is wrong. Lipschitz continuity implies $\|f(x) - f(y)\| \leq M\|x - y\|$ for "some" $M > 0$ where $M$ is called the Lipschitz "constant". Thereby, in your proof you "cannot choose" $M = \epsilon/\delta$. However, remember that you can choose $\epsilon$ and $\delta$. Also, Lipschitz continuity implies uniform continuity, which is what you are ending up proving.
Nov 28	comment	Closest vector problem for orthogonal lattices ah yes you are right. Apologies, I was truly confused by the wording given there. Sorry about that.
Nov 26	comment	Closest vector problem for orthogonal lattices I thought the second paragraph there was what you asked for (Though, there is a typo in that line which needs to be fixed)?