THE NUMERICAL RANGE OF 3X3 MATRICES

Authors
KEELER DS RODMAN L SPITKOVSKY IM
Citation
Ds. Keeler et al., THE NUMERICAL RANGE OF 3X3 MATRICES, Linear algebra and its applications, 252, 1997, pp. 115-139
Citations number
10
Categorie Soggetti
Mathematics,Mathematics
Journal title
Linear algebra and its applications → ACNP
ISSN journal
00243795
Volume
252
Year of publication
1997
Pages
115 - 139
Database
ISI
SICI code
0024-3795(1997)252:<115:TNRO3M>2.0.ZU;2-L
Abstract
Let A be an n x n complex matrix. Then the numerical range of A, W(A), is defined to be {xAx : x is an element of C-n, x*x = 1}. In this ar ticle a series of tests is given, allowing one to determine the shape of W(A) for 3 x 3 matrices. Reconstruction of A, up to unitary similar ity, from W(A) is also examined. (C) Elsevier Science Inc., 1997