# Tagged Questions

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### exact definition of Fiedler vector

For a given N-vertex similarity graph $G=(V,A)$ the eigenvalues of the unrenormalized (graph) Laplacian may be denoted as $$0= \mu_0 \leq \mu_1 \leq ... \leq \mu_N$$ where the corresponding ...
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### Spectral radius of a non-negative matrix after moving and replicating an element

Let $A$ be a non-negative square matrix and its spectral radius (i.e., it's largest eigenvalue) be $\rho(A)$. I need to do the following operation to $A$ and compare the resulting spectral radii. ...
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### Conditions for continuity of non-simple eigenvectors

Here, http://math.stackexchange.com/a/1146455, it is noted that eigenprojections are continuous, but eigenvectors are not. Are there any conditions where the eigenvalues are not simple, but the ...
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### Spectral radius's relation with row sum

Let $A$ be a non-negative $N \times N$ square matrix with $a_{i,i}=0, 1 \leq i \leq N$. Also, let $r_i$ be the $i$-th row sum of $A$. I know that $\rho(A)$, the spectral radius of $A$, is bounded as ...
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### Non-asymptotic bound on the variance of largest singular value of gaussian matrix

Let $A$ be a gaussian matrix of size $d \times n$ where all the coefficients are drawn i.i.d. from $\mathcal{N}(0, 1)$ and denote by $s_{\text{max}}$ its largest singular value. Theorem 2.6 of http:/...
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### Extension of Wigner's semicircle law?

It is well-known that the semicircle law holds for a wide class of matrices with independent and identically distributed (mean zero) entries. My question is: is there any study about the more general ...