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Results tagged with spectral-radius
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user 1898
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.
3
votes
Accepted
Lower spectral radius of matrices with an invariant subspace
This is false; the result is not perfectly analogous because the definition of the spectral radius contains a maximum. Here is a counterexample.
Take
$$
A_1 = \begin{bmatrix}2 & 0\\ 0 & 1\end{bmatrix} …
- 20.2k
9
votes
Accepted
spectral radius monotonicity
Not true in general, as noted by @SergeiIvanov, but true for (element-wise) nonnegative matrices.
Note that if $\rho(S) < b$, then $b(bI-S)^{-1}=(I-\frac{S}{b})^{-1}=\sum_{i=0}^\infty \frac{S^i}{b^i} …
- 20.2k
3
votes
Projecting onto space of matrices with spectral radius less than one
For the version without the absolute value, a colleague and I published a few months ago an algorithm to solve that optimization problem and other related ones (the problem you need is called "Schur s …
- 20.2k