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The numerical range of 3 × 3 matrices

1997; Elsevier BV; Volume: 252; Issue: 1-3 Linguagem: Inglês

10.1016/0024-3795(95)00674-5

1873-1856

Dennis S. Keeler, Leiba Rodman, Ilya M. Spitkovsky,

Statistical and numerical algorithms

Let A be an n × n complex matrix. Then the numerical range of A, W(A), is defined to be {x∗Ax: x ∈ Cn, x∗x = 1}. In this article a series of tests is given, allowing one to determine the shape of W(A) for 3 × 3 matrices. Reconstruction of A, up to unitary similarity, from W(A) is also examined.