A non-negative matrix is one whose entries are non-negative.
A non-negative matrix $M$ is such that $m_{ij}\geq 0$. The Perron-Frobenius theorem asserts the existence of a unique largest positive eigenvalue of non-negative matrices.
Questions tagged [nonnegative-matrices]
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Does this function preserve the order of the nonnegative matrices
Suppose A and B are nonnegative matrices, that is, $A\geq 0$ and $B\geq 0$. Moreover, suppose $\|A\|_{\infty}<1, \|B\|_{\infty}<1$ and $A\leq B$. For $f(x)=x(2-x)$, we know that $f(x)$ is increasing in $(0,1)$. I wonder if it is true that $f(A)\leq…
