Question
Let $A$ be a square matrix. Let $s=\max \left\{s_1, \ldots, s_n\right\}$ be the maximal absolute row sum of $A$ and let $t=\min \left\{\left|a_{i i}\right|-r_i\right\}$, with $r_i$ given by (8.27). Prove that $\max \{0, t\} \leq \rho(A) \leq$ s.
Step 1
- Let $A$ be an $n \times n$ matrix with elements $a_{ij}$. - Define $s_i = \sum_{j=1}^n |a_{ij}|$ as the sum of the absolute values of the elements in the $i$-th row of $A$. - Define $s = \max \{s_1, \ldots, s_n\}$ as the maximum absolute row sum of $A$. - Define Show more…
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Symmetric Matrices and Quadratic Forms
Constrained Optimization
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