1,526 reputation
410
bio website cse.iitb.ac.in/~aruniyer
location India
age 30
visits member for 2 years, 2 months
seen 1 hour ago

Jul
22
asked What is a set function that returns another set of points called?
Jul
21
comment If A is a balanced subset $\Longrightarrow$ conv$(A)$ is balanced
Your $C$ is not defined correctly. Define $C$ as $C = \{\sum_{i = 1}^{|A|}a_ix_i : a_i \geq 0 \forall i, \sum_{i = 1}^{|A|} a_i = 1, x_i \in A \forall i\}$. Proving that this is convex is very easy. You should also be able to show that this is equal to conv(A) very easily.
Jul
19
comment How to prove that $\frac{\sin \pi x}{\pi x}=\prod_{n=1}^{\infty}(1-\frac{x^2}{n^2})$
You should probably read this excellent article :-) cornellmath.wordpress.com/2007/07/13/…
Jul
16
comment What does a space mean?
@user50229 Thanks :-)
Jul
13
revised $F(u)= \frac{2}{\pi}\int_{0}^\infty \frac{uf(x)}{u^2 + x^2}dx.$ Show that $\lim\limits_{u\downarrow0}F(u)=f(0)$.
Fixed an error in the title
Jul
13
suggested suggested edit on $F(u)= \frac{2}{\pi}\int_{0}^\infty \frac{uf(x)}{u^2 + x^2}dx.$ Show that $\lim\limits_{u\downarrow0}F(u)=f(0)$.
Jul
9
comment approximation of the sum of matrices
You can show that $\|r_i \nabla^2r_i\| \leq \epsilon$. This would imply that $\|H - \tilde{H}\| \leq \epsilon$.
Jun
22
comment properties of two positive definite matrix
@miosaki you have already shown if A is positive definite then A^2 is positive definite. Similarly, B^2 is positive definite. Also, you know that if X and Y are positive definite, then X + Y is positive definite. If you put X as A^2 and Y as B^2, what do you get?
May
7
awarded  Caucus
Apr
23
awarded  Yearling
Mar
27
answered Why do we use gradient descent in the backpropagation algorithm?
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.
Mar
8
answered Intuition behind logarithm inequality
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?
Feb
6
answered Is a convex, nondecreasing function of an invex function invex?
Feb
2
suggested suggested edit on Positive definite matrix inequality
Feb
2
answered What does it mean to restricting a function to a line in convex optimization?
Jan
27
comment How variance is defined?
What you propose is another way of measuring spread - it is called mean absolute deviation.