TY - JOUR
T1 - The product field of values
AU - Corey, Daniel
AU - Johnson, Charles R.
AU - Kirk, Ryan
AU - Lins, Brian
AU - Spitkovsky, Ilya
N1 - Funding Information:
This work was partially supported by NSF Grant DMS-0751964. Corresponding author. Address: Hampden-Sydney College, Box 131, Hampden-Sydney, VA 23943, United States. Tel.: +1 434 223 6264. E-mail addresses: [email protected] (D. Corey), [email protected] (C.R. Johnson), [email protected] (R. Kirk), [email protected] (B. Lins), [email protected].
PY - 2013/3/1
Y1 - 2013/3/1
N2 - For two n-by-n matrices, A,B, the product field of values is the set P(A,B)={〈Ax,x〉〈Bx,x〉:x∈Cn,||x||=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.
AB - For two n-by-n matrices, A,B, the product field of values is the set P(A,B)={〈Ax,x〉〈Bx,x〉:x∈Cn,||x||=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.
KW - Field of values
KW - Numerical range
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U2 - 10.1016/j.laa.2012.09.028
DO - 10.1016/j.laa.2012.09.028
M3 - Article
AN - SCOPUS:84872100952
SN - 0024-3795
VL - 438
SP - 2155
EP - 2173
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 5
ER -