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- W2034239214 abstract "Let A be an n × n complex matrix and c = ( c 1 , c 2 , … , c n ) a real n -tuple. The c -numerical range of A is defined as the set W c ( A ) = ∑ j = 1 n c j x j ∗ Ax j : { x 1 , x 2 , … , x n } is an orthonormal basis for C n . When c = ( 1 , 0 , … , 0 ) , W c ( A ) becomes the classical numerical range of A which is often defined as the set W ( A ) = { x ∗ Ax : x ∈ C n , x ∗ x = 1 } . We show that for any n × n complex matrix A and real n -tuple c , there exists a complex matrix B of size at most n ! such that W c ( A ) = W ( B ) . Constructions of the matrix B for some matrices A and real n -tuple c are provided." @default.
- W2034239214 created "2016-06-24" @default.
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- W2034239214 date "2011-02-01" @default.
- W2034239214 modified "2023-09-30" @default.
- W2034239214 title "Reduction of the c-numerical range to the classical numerical range" @default.
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- W2034239214 doi "https://doi.org/10.1016/j.laa.2010.09.010" @default.
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