0
$\begingroup$

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?
$\endgroup$
1
  • $\begingroup$ 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

1
$\begingroup$

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.

$\endgroup$
2
  • $\begingroup$ And symmetric. [filler] $\endgroup$ Commented Jun 8, 2016 at 18:25
  • $\begingroup$ Yes, thank you! $\endgroup$
    – Siminore
    Commented Jun 8, 2016 at 18:44

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .