#### Title

#### Document Type

Article

#### Publication Date

10-1-1988

#### Published In

SIAM Journal On Matrix Analysis And Applications

#### Abstract

Let A be a nonnegative, n n matrix, and let b be a nonnegative, nxn vector. Let S be the sequence {Akb }, k = 0, l, 2, .... Define m(A, b) to be the length of the cycle of zero-nonzero patterns into which S eventually falls. Define m(A) to be the maximum, over all nonnegative b of m(A, b). Finally, define m(n) to be the maximum, over all nonnegative, nxn matrices A of m(A). This paper shows given A and b, that m(A, b) is a divisor of a certain number, which is determined by the structure of A and b. It is also shown that log m(n) ~ (n log n) /2.

#### Recommended Citation

Charles M. Grinstead.
(1988).
"Cycle Lengths In Aᵏb".
*SIAM Journal On Matrix Analysis And Applications*.
Volume 9,
Issue 4.
537-542.

https://works.swarthmore.edu/fac-math-stat/59

## Comments

This work is freely available courtesy of the Society for Industrial and Applied Mathematics.