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The <group (mathematics)> of all transformations that preserve some <bilinear form>, notable examples:
* <orthogonal group> preserves the <inner product>
* <unitary group> preserves a <Hermitian form>
* <Lorentz group> preserves the <Minkowski inner product>


Isometry group

{c}
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The <complex number> analogue of a <symmetric bilinear form>.

The prototypical example of it is the <complex dot product>.

Note that this form is neither strictly <symmetric bilinear map>[symmetric], it satisfies:
$$
<x, y> = \overline{<y, x>}
$$
where the over bar indicates the <complex conjugate>, nor is it linear for complex scalar multiplication on the second argument.

Bibliography:
* https://mathworld.wolfram.com/HermitianForm.html


Ciro Santilli @cirosantilli 37

 Incoming links: Hermitian form