Linear Algebra by Jörg Liesen & Volker Mehrmann
Author:Jörg Liesen & Volker Mehrmann
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham
The prefix sesqui is Latin and means “one and a half”. Note that a sesquilinear form is linear in the first variable and semilinear (“half linear”) in the second variable.
The following result characterizes Hermitian sesquilinear forms.
Lemma 11.18
A sesquilinear form on the -vector space is Hermitian if and only if for all .
Proof
If s is Hermitian then, in particular, for all , and thus .
If, on the other hand, , then by definition
(11.1)
(11.2)
The first equation implies that , since by assumption. The second equation implies analogously that . Therefore,
Download
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.
Linear Algebra for Computational Sciences and Engineering by Ferrante Neri(457)
Numerical Linear Algebra and Matrix Factorizations by Tom Lyche(423)
Linear Algebra and Its Applications by Peter D. Lax(391)
Nonnegative Matrices and Applicable Topics in Linear Algebra by Alexander Graham(322)
Linear Algebra and Optimization for Machine Learning by Charu C. Aggarwal(310)
Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Pavel Grinfeld(301)
A Matrix Algebra Approach to Artificial Intelligence by Xian-Da Zhang(295)
Introduction to Linear Algebra by Frank M. Stewart(273)
The Jossey-Bass Handbook of Nonprofit Leadership and Management by David O. Renz(270)
Linear Algebra by Jörg Liesen & Volker Mehrmann(248)
Galois Theory and Advanced Linear Algebra by Rajnikant Sinha(230)
EXCEL 2019: A Quick And Easy Guide To Master Spreadsheets And Boosting Productivity, With Tips And Tricks To Make Easier The use Of Excel Thanks To The Keyboard Commands by Jones Edward(182)
