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Results tagged with limits-and-convergence
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user 130361
Convergence of series, sequences and functions and different modes of convergence.
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Matrix iteration for non-negative matrices. Does it converge to some eigenvector?
Let $A$ be a non-negative (entrywise) matrix such that $A(1,1)>0$. Set $u=(1,0,0,...,0)^T$. Is it always true that there exists a non-negative eigenvector $v$ of $A$ such that $\lim_{n\rightarrow\inft …
- 21
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Accepted
Matrix iteration for non-negative matrices. Does it converge to some eigenvector?
The statement is not true. Let $a>1$ and define
\begin{equation}
A:=\begin{bmatrix}1&0&0\\1&0&a\\0&a&0 \end{bmatrix}.
\end{equation}
Suppose there is $v\in\mathbb{R}^n\backslash\{0\}$ such that $\l …
- 21