In mathematics, the spectral radius of a square matrix or a bounded linear operator is the supremum among the absolute values of the elements in its spectrum.

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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 $\rho(M)$ ...
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### Upper bounds on absolute eigenvalue of sum of two matrix

We have this iteration $$X_{k+1}=(G\cdot Jf+H)X_k+C$$ with $G$ is symmetric and nonnegative, $H$ is nonnegative. $Jf$ is the jacobian matrix of some function $f$ and we can assume it satisfy certain ...
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### Minimize spectral norm under diagonal similarity

Let $A$ be a real square matrix of size $n \times n$. Is there an upper bound on the minimum spectral norm under diagonal similarity, i.e., $$s(A) = \min_{D} \lVert D^{-1} A D\rVert_2,$$ where $D$ ...
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Let $A$ be a $C^*$ algebra. Let $a\in A$ be such that $a^*a-aa^*\geq 0$. Doe this imply that the spectral radius of $a$ is equal to $\|a\|$?
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### The spectral radius of a binary matrix

Let $\mathcal B_n$ denote the set of $n\times n$ matrices with entries in $\{0,1\}$. It follows from the spectral radius formula that if $M\in\mathcal B_n$ is not nilpotent, then $\rho(M)$, the ...
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### best known bounds for spectral radius [closed]

There are many bounds for the spectral radius of graphs in terms of no. of vertices, maximum degree, chromatic number etc. I wish to know till date what are the best lower and upper bound for the ...
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### Spectral radius of the product of a right stochastic matrix and a block diagonal matrix

Let us define the following matrix: $C=AB$ where $B$ is a block diagonal matrix with $N$ blocks, $B_1$, $B_2$ … $B_N$, each of dimensions $M \times M$. I know that $B_k = I_M - \mu R_k$ with $R_k$ ...
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### Operator norm vs spectral radius for positive matrices

I believe the following statement should be true but somehow I don't see an argument: For every integer $d>1$ there exists a constant $C=C(d)>1$ such that whenever $A$ is a $d \times d$ matrix ...
Hi I would like to solve the following optimization problem. Let $A$ be an $n \times n$ nonnegative real matrix where $A^{-1}$is an M-matrix. Let $D=\text{diag}\{d_{1}, \dots , d_{n}\}$ be a ...