A simple proof of the convexity of the field of values defined by two Hermitian forms

DOI10.1007/BF01834040zbMath0307.15009MaRDI QIDQ1217760

Yik-Hoi Au-Yeung

Publication date: 1975

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/136483

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Hermitian, skew-Hermitian, and related matrices (15B57) Quadratic and bilinear forms, inner products (15A63)

Related Items

Theory of optimal control in the works of V.A. Yakubovich, Generalized numerical ranges, joint positive definiteness and multiple eigenvalues, Linear combinations of Hermitian and real symmetric matrices, Elliptic quadratic operator equations, Some theorems on the generalized numerical ranges, Computer generated numerical ranges and some resulting theorems, A recurring theorem about pairs of quadratic forms and extensions: A survey, Joint zero sets and ranges of several Hermitian forms over complex and quaternionic scalars, Joint matricial range and joint congruence matricial range of operators

Cites Work

• Convexity of the Field of a Linear Transformation
• On the Field of Values of a Matrix
• A Theorem on a Mapping from a Sphere to the Circle and the Simultaneous Diagonalization of Two Hermitian Matrices