All Questions
Tagged with lower-bounds matrices
9 questions
2
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0
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Extension of the Gershgorin circle theorem for symmetric matrices and localization of positive eigenvalues
In mathematics, the Gershgorin circle theorem can be used to localize eigenvalues of a matrix (including symmetric). Let $A$ be a real symmetry $n × n$ matrix, with entries $a_{ij}$. For $i∈{1,…,n}$ ...
- 145
6
votes
2
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259
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Distance of low-rank matrices to the identity for the $\infty$-norm
I am trying to get a lower bound (or even the exact value) of
$$
\min_{X \in \mathbb{R}^{n\times n}} \|X - I_n\|_{\infty} \enspace \text{s.t.} \enspace \mbox{Rank}(X) = m
$$
where $m \leq n$, and the ...
- 197
2
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1
answer
680
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Is this lower bound on the singular values of the sum of two matrices correct?
Equation 7 of this paper (Ramazan Türkmen, Zübeyde Ulukök, Inequalities for Singular Values of Positive Semidefinite Block Matrices, International Mathematical Forum, Vol. 6, 2011, no. 31, 1535 - 1545)...
2
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1
answer
447
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How to find upper and lower bound
Let $\Sigma \in S_{++}^n$ be a symmetric positive definite matrix with all diagonal entries equal to one. Let $U \in \mathbb{R}^{n \times k_1}$, $W \in \mathbb{R}^{n \times k_2}$, $\Lambda \in \mathbb{...
- 61
0
votes
1
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262
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Survey papers on spectral radius [closed]
Let $M$ be a $n\times n$ matrix.
Are there any survey papers which give lower and upper bounds on its spectral radius?
What are the ways to find some lower bounds and upper bounds on $\rho(M)$ ...
- 444
2
votes
1
answer
140
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Minimum local permutation data needed to globally merge locally sorted sequences?
We have $k$ blocks of integer sequences $B_1,\dots,B_k$ where $B_i$ is a sequence $$a_{i,1},\dots,a_{i,n_i}$$ with $a_{i,j}\leq a_{i,j+1}$.
Denote the permutation matrix $M_{\ell,\ell'}$ that merges $...
- 1,826
6
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2
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1k
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Nontrivial lower bound on the sum of matrix norms
Let $X, V\in\mathbb{R}^{n\times r}$ such that $X^\top V$ is symmetric. The central quantity I care about is
\begin{equation}
\|XV^\top\|_{F}^2+\|X^\top V\|_{F}^2 +[\text{Tr}(X^\top V)]^2.
\end{...
- 515
2
votes
0
answers
411
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Bound on eigenvalues of A+B (Hermitan matrices) which is better that the Lidskii and Weyl bounds
I have two positive definite $N\times N$ Hermitian matrices $A$ and $A$ and am interested in bounding the eigenvalues of $A+B$ in terms of the eigenvalues of $A$ and $B$. Let $\lambda_k(\cdot)$ be ...
1
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0
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148
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Bounding the Schur's complement of similiar matrices
Assume the following:
• $L\leq K$
.
• $\Gamma\in M_{K,L}$ is a $L$ rank ${ 0,1} $ matrix, without identical rows or the zeros row.
• $N\in M_{K,K}$ is a diagonal matrix, whose diagonal is a ...
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