All Questions
8 questions with no upvoted or accepted answers
7
votes
0
answers
217
views
Characterizing matrices with rank constraint
Given matrix $M\in\Bbb\{0,1\}^{n\times n}$, is there a nice method to characterize $$\mathscr{D}[M]=\{Q\in\Bbb\{0,1\}^{n\times n}:\mathsf{rank}(M-Q)= \mathsf{rank}(Q),\quad M-Q\in\Bbb\{0,1\}^{n\times ...
- 13.9k
2
votes
1
answer
506
views
Effect of duplicated row on singular values and vectors
Let $\mathbf{A}$ be a $n\times n$ matrix with Singular Value Decomposition (SVD) $\mathbf{A}=\mathbf{U}\mathbf{S}\mathbf{V}$ and $\mathbf{a}_1$ be the first row of $\mathbf{A}$. What can we say about ...
- 287
2
votes
0
answers
156
views
Optimization of quadratic form with band matrices
Let $A_1$ be the $N \times N$-matrix for which $a_{i,j} = 1$ for $i=j$ and 0 otherwise. Let $A_2$ be the matrix for which $a_{i,j}=1$ for $|i-j| \leq 1$ and 0 otherwise. Similarly define $A_3$ (which ...
- 2,207
1
vote
0
answers
150
views
Minimax optimization of diagonal entries of function of matrix
Let $\mathbf{A}$ and $\mathbf{U}$ be arbitrary complex $M\times N$ and $N\times M$ matrices, respectively. Let denote superscript $(\cdot)^{\dagger}$ and $(\cdot)^{\mathrm{H}}$ as pseudo-inverse and ...
- 287
1
vote
0
answers
138
views
Matrix completion in $2\times2$ case by nuclear norm minimization to guarantee rank $1$?
Does fixing diagonal entries and minimizing nuclear norm under weighted sum of entries conditions produce a rank $1$ matrix? I think the answer for this is no.
At least could it be true in $2\times2$ ...
- 13.9k
0
votes
0
answers
52
views
What are the injective embeddings of R^d into the cone of (semi-) positive definite matrices of dimension d?
How can we characterize the set of all injective functions from $\mathbb{R}^d$ to the set of all symmetric positive definite matrices of dimension d?
- 109
0
votes
0
answers
72
views
Minimizing the Spectral Norm of the Hadamard Product of a Quadratic Form Using CVX
I am trying to use CVX to minimize the spectral norm of the Hadamard product of two matrices, one of which is in quadratic form. Specifically, I am trying to minimize $\|{\bf A} \odot {\bf XX}^H\|_2$, ...
- 43
0
votes
0
answers
52
views
Dense Matrix Estimation
I have a matrix $X \in \mathbb{R}^{m\times n}$ and I want to estimate it with a dense matrix $Y^{m\times n}$ such that $Y$ is still close to $X$ in some distance measure. Is this doable in a ...
- 137