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On a complex vector space a sesquilinear map is a function of two arguments
which is a linear function in one argument (say the second) and complex anti-linear in the other.
A sesquilinear form is called
Finally, it is called indefinite if it is neither positive nor negative semi-definite.
More generally:
Let be a star algebra. Then every left -module canonically becomes a right module by setting
and vice versa.
With this operation understood to turn a left module into a right module, then a sesquilinear form on is simply an element in the tensor product of modules
of the -linear dual of with itself.
See also:
Brian Osserman, A primer on sesquilinear forms (pdf)
Wikipedia, Sesquilinear form
Last revised on May 4, 2021 at 03:54:38. See the history of this page for a list of all contributions to it.