Answer by user539887 for Bound on the norm of a matrix power
Let $\lVert \cdot \rVert$ be a matrix norm on $\mathbb{C}^{n \times n}$. I assume that we know Gelfand's formula:$$\rho(A) = \lim\limits_{k\to\infty}\lVert A^k\rVert^{1/k}.$$We want to prove that for...
View ArticleBound on the norm of a matrix power
Suppose we have the square matrix $A$ and we know that its spectral radius $\rho(A)$ is less than $1$, therefore matrix $A$ is stable. How can we prove that $\exists \gamma \in(0,1)$ and $\exists M...
View ArticleAnswer by Lorenzo Pompili for Bound on the norm of a matrix power
I have been asked to explain things better.The formula in the question holds for all $\gamma>\rho(A)$ and some $M>0$ which depends on $\gamma$ (… and on $A$, as shown in the end), as it has been...
View Article
More Pages to Explore .....
