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The product field of values
Corey, Daniel Johnson, Charles R. Spitkovsky, Ilya Kirk, Ryan Lins, Brian
Corey, Daniel
Johnson, Charles R.
Spitkovsky, Ilya
Kirk, Ryan
Lins, Brian
Abstract
For two n-by-n matrices, A, B, the product field of values is the set P(A, B) = {< AX, X > < Bx, X > : X is an element of C-n, parallel to X parallel to = 1}. In this paper, we establish basic properties of the product field of values. The main results are a proof that the product field is a simply connected subset of the complex plane and a characterization of matrix pairs for which the product field has nonempty interior. (C) 2012 Elsevier Inc. All rights reserved.
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2013-01-01
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Corey, D., Johnson, C. R., Kirk, R., Lins, B., & Spitkovsky, I. (2013). The product field of values. Linear Algebra and its Applications, 438(5), 2155-2173.
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Mathematics
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10.1016/j.laa.2012.09.028