I understand that the inner product of two vectors and its properties. However I do not quite understand bilinear mappings.

  • What is the relationship between inner products and bilinear mapping?
  • and how could I use this to show that two inner products <x,y> and <u,v> of vector space V have bases which are orthogonal to both inner products?
  • $\begingroup$ A bilinear mapping is a function of two vectors that is linear in each "slot". $\endgroup$ Commented Jun 8, 2016 at 18:20

1 Answer 1


An inner product is a particular bilinear form, at least when the field is $\mathbb{R}$. It has the additional property of being positive-definite and symmetric.

  • $\begingroup$ And symmetric. [filler] $\endgroup$ Commented Jun 8, 2016 at 18:25
  • $\begingroup$ Yes, thank you! $\endgroup$
    – Siminore
    Commented Jun 8, 2016 at 18:44

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