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| Titel: |
On the sum powers of matrices |
| Auteur: |
Vaserstein, L. N. |
| Verschenen in: |
Linear & multilinear algebra |
| Paginering: | Jaargang 21 (1987) nr. 3 pagina's 261-270 |
| Jaar: |
1987-11 |
| Inhoud: |
A theorem of Lagrange says that every natural number is the sum of 4 squares. M. Newman proved that every integral n by n matrix is the sum of 8 (-1)n squares when n is at least 2. He asked to generalize this to the rings of integers of algebraic number fields. We show that an n by n matrix over a a commutative R with 1 is the sum of squares if and only if its trace reduced modulo 2Ris a square in the ring R/2R. It this is the case (and n is at least 2), then the matrix is the sum of 6 squares (5 squares would do when n is even). Moreover, we obtain a similar result for an arbitrary ring R with 1. Answering another question of M. Newman, we show that every integral n by n matrix is the sum of ten k-th powers for all sufficiently large n. (depending on k). |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 11 van 16 gevonden artikelen
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