# inner product and bilinear mappings

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?
• A bilinear mapping is a function of two vectors that is linear in each "slot". – Tyler Gaona Jun 8 '16 at 18:20

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.

• And symmetric. [filler] – Gunnar Þór Magnússon Jun 8 '16 at 18:25
• Yes, thank you! – Siminore Jun 8 '16 at 18:44