Bilinear form Totally Explained

Everything about Skew-symmetric Bilinear Form totally explained

In mathematics, a bilinear form on a vector space V is a bilinear mapping V × V → F, where F is the field of scalars. That is, a bilinear form is a function B: V × V → F which is linear in each argument separately: ť

egin.

Likewise, symmetric bilinear forms may be thought of as elements of S²V* (the second symmetric power of V*), and alternating bilinear forms as elements of Λ²V* (the second exterior power of V*).

On normed vector spaces

A bilinear form on a normed vector space is bounded, if there's a constant

C

such that for all

u, vin V

B(u,v) le C |u| |v|.

A bilinear form on a normed vector space is elliptic, or coercive, if there's a non-zero constant

c

such that for all

uin V

B(u,u) ge c |u|^2.

Further Information

Get more info on 'Skew-symmetric Bilinear Form'.

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