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?
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.