Bilinear form | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-03-25

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Bilinear_form


00:00:17 1 Coordinate representation
00:00:35 2 Maps to the dual space
00:01:09 3 Symmetric, skew-symmetric and alternating forms
00:02:40 4 Derived quadratic form
00:04:15 5 Reflexivity and orthogonality
00:04:40 6 Different spaces
00:05:49 7 Relation to tensor products
00:06:47 8 On normed vector spaces
00:06:51 9 Generalization to modules
00:09:02 10 See also
00:09:41 11 Citations
00:09:50 12 References
00:10:01 13 External links
00:10:58 0 ⇔ xTA
00:11:57 Different spaces
00:14:26 4, then Lorentzian space is also called Minkowski space or Minkowski spacetime. The special case R(p, p) will be referred to as the split-case.
00:14:37 Relation to tensor products
00:15:27 On normed vector spaces
00:16:27 Generalization to modules
00:17:39 See also



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SUMMARY
=======
In mathematics, a bilinear form on a vector space V is a bilinear map V × V → K, where K is the field of scalars.  In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately:

B(u + v, w) = B(u, w) + B(v, w)     and     B(λu, v) = λB(u, v)
B(u, v + w) = B(u, v) + B(u, w)     and     B(u, λv) = λB(u, v)The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms.
When K is the field of complex numbers C, one is often more interested in sesquilinear forms, which are similar to bilinear forms but are conjugate linear in one argument.