Some Results on the Generalized Higher Rank Numerical Ranges
نویسنده
چکیده
In this paper, the notion of rank−k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for > 0, the notion of Birkhoff-James approximate orthogonality sets for −higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed definitions yield a natural generalization of the standard higher rank numerical ranges. Keywords—Rank−k numerical range, isometry, numerical range, rectangular matrix polynomials.
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