Geometric Motivation
Bilinear forms are to squaring (z2), what sesquilinear forms are to Euclidean norm (|z|2 = z*z).
The norm associated to a sesquilinear form is invariant under multiplication by the complex circle (complex numbers of unit norm), while the norm associated to a bilinear form is equivariant (with respect to squaring). Bilinear forms are algebraically more natural, while sesquilinear forms are geometrically more natural.
If B is a bilinear form on a complex vector space and is the associated norm, then .
By contrast, if S is a sesquilinear form on a complex vector space and is the associated norm, then .
Read more about this topic: Sesquilinear Form
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