Numerical range of a pair of strictly upper triangular matrices
Given two strictly upper triangular matrices X, Y ? Cm×m, we study the range W Y (X) = {trnXn-1Y* : n ? N}, where N is the group of unit upper triangular matrices in Cm×m. We prove that it is either a point or the whole complex plane. We characterize when it is a point. We also obtain some convexity result for a similar range, where N is replaced by any ball of Ck (k = m(m - 1)/2) embedded in N , m = 4.
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| Format: | Digital revista |
| Language: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2011
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000100008 |
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