Hermitian form
A sesquilinear form over a pair of complex vector spaces is a function satisfying the following properties:
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1.
-
2.
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3.
for all , , and . The vector spaces and are often identical, although the definition does not require them to be the same vector space.
A sesquilinear form over a single vector space is called a Hermitian form if it is complex conjugate symmetric: namely, if .
An inner product over a complex vector space is a positive definite Hermitian form.
Title | Hermitian form |
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Canonical name | HermitianForm |
Date of creation | 2013-03-22 12:25:47 |
Last modified on | 2013-03-22 12:25:47 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 8 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 47A07 |
Classification | msc 15A63 |
Classification | msc 11E39 |
Synonym | sesquilinear form |
Synonym | sesqui-linear form |
Related topic | InnerProduct |