๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

When is a pair of matrices mortal?

โœ Scribed by Vincent D. Blondel; John N. Tsitsiklis

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
379 KB
Volume
63
Category
Article
ISSN
0020-0190

No coin nor oath required. For personal study only.

โœฆ Synopsis

A set of matrices over the integers is said to be k-morrul (with k positive integer) if the zero matrix can be expressed as a product of length k of matrices in the set. The set is said to be mortal if it is k-mortal for some finite k. We show that the problem of deciding whether a pair of 48 x 48 integer matrices is mortal is undecidable, and that the problem of deciding, for a given k, whether a pair of matrices is k-mortal is NP-complete. @

๐Ÿ“œ SIMILAR VOLUMES

The boundedness of all products of a pai
The boundedness of all products of a pair of matrices is undecidable
โœ Vincent D. Blondel; John N. Tsitsiklis ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 97 KB

We show that the boundedness of the set of all products of a given pair of rational matrices is undecidable. Furthermore, we show that the joint (or generalized) spectral radius ( ) is not computable because testing whether ( )61 is an undecidable problem. As a consequence, the robust stability of l

When a 12.86% mortality is more dangerou
When a 12.86% mortality is more dangerous than 24.14%: implications for risk communication
โœ Kimihiko Yamagishi ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 164 KB

Participants assessed the riskiness of 11 well-known causes of death. Each participant was presented with an estimation of the number of deaths in the population due to that particular cause. The estimates were obtained from a previous study of naive participants' intuitive estimations. For instance

Person-time analysis of paired community
Person-time analysis of paired community intervention trials when the number of communities is small
โœ Ron Brookmeyer; Ying-Qing Chen ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 119 KB

Community intervention trials involve randomization of communities to either an intervention or control arm. The objective of this paper is to evaluate person-time methods of analysis of paired community intervention trials when the number of community pairs is small. We consider several test proced