2018
Том 70
№ 6

All Issues

Expressing infinite matrices as sums of idempotents

Słowik R.


Abstract

Let $\scr M_{Cf} (F)$ be the set of all column-finite $N \times N$ matrices over a field $F$. The following problem is studied: what elements of $\scr M_{Cf} (F)$ can be expressed as a sum of idempotents? The result states that every element of $\scr M_{Cf} (F)$ can be represented as the sum of 14 idempotents.

Citation Example: Słowik R. Expressing infinite matrices as sums of idempotents // Ukr. Mat. Zh. - 2017. - 69, № 8. - pp. 1145-1147.