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Indian Institute of Science


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comment Every invertible linear transformation can be perturbed a bit without destroying invertbility, Neumann series
The argument seems correct to me also. I am wondering why it is getting so many downvotes without any explanation?
Dec
16
awarded  Caucus
Dec
13
comment Does this equations represent the sphere?
ok. Can you write this as an answer?? I will accept it.
Dec
13
comment Does this equations represent the sphere?
does it sum to 1?
Dec
13
revised Does this equations represent the sphere?
added 2 characters in body; edited title
Dec
13
asked Does this equations represent the sphere?
Dec
8
comment If matrix $\sum_0^\infty C^k$ is convergent, how can I prove that $A(\sum_0^\infty C^k)B$ is convergent?
+1, nice!. would you be kind enough to give a reference for this?
Dec
5
comment A interesting max min problem
so, you are saying that $c_1^{\star}\leq c_2^{\star}$ in general. For that particular choice of $\mathcal{S}$ you made, they are equal, Though, in general, it is not so.
Dec
4
comment A interesting max min problem
The argument in the last comment you put forward is what confused me actually. For a given $t$, I have to select a $(x_1,x_2)\in\mathcal{S}$. When I go to a new $t$, won't this $x_2$ change? So how does this unboundedness happen. Also, note that $\lambda(t)$ is a concave function. If you assume there is a point which attains the maximum, then if you move away from $t$, shouldn't it decrease?
Dec
4
comment Projection matrices identity: $P_{M_ZX}=P_{M_Zx}+P_{M_{[x\; Z]}X_2}$
So $P_{AB}$ is the projection matrix corresponding to the product of matrices $A$ and $B$ (with conforming dimensions)?
Dec
4
comment A interesting max min problem
So whether $c_2^{\star}\leq c_1^{\star}$ will depend on the nature $\mathcal{S}$, is that what you are saying?
Dec
4
comment A interesting max min problem
Isn't $\lambda(t)$ the minimum over $(x_1,x_2)\in\mathcal{S}$ for a given $t$?
Dec
4
comment A interesting max min problem
@RossMillikan yes, I corrected the question accordingly.
Dec
4
revised A interesting max min problem
deleted 12 characters in body
Dec
3
asked A interesting max min problem
Dec
1
comment Sum of k-largest eigenvalues of a symmetric matrix as an SDP
Can you please take a look at the comment I have posted on the OP's question? does it help?
Dec
1
comment Sum of k-largest eigenvalues of a symmetric matrix as an SDP
btw, I guess $X$ should be non-negative definite for the above argument to work, if it works at all!!
Dec
1
comment Sum of k-largest eigenvalues of a symmetric matrix as an SDP
can we think like this? Say $s=0$, then $Z\geq X$ implies $trace(Z)\geq trace(X)$ (can't see a way to prove it though!!). Then $t\geq trace(Z)\geq trace(X) \geq S_k(X)$.
Dec
1
comment Sum of k-largest eigenvalues of a symmetric matrix as an SDP
+1, Then $\mathbf{A}$ will be the sum of $k$ rank-one positive semi-definite matrices, where each matrix is the outer product of unit-norm eigenvectors corresponding to the $k$ largest eigenvalues, Is that the idea?
Nov
27
revised iid Gaussian random matrix $A\in M_n$ has full rank with probability 1?
added 41 characters in body