How to determine the following statement is bilinear mapping or not?

Question

I have already checked wikipedia about bilinear mapping but still I haven't figured out how these things are working. Could anyone explain me?

Thanks in advance for your help.

bilinear mapping or not

Answer 1

A function of two vectors in a vector space is bilinear if it is linear w. r. t. each of these vectors.

Two examples:

• The dot product in $\mathbf R^2$ or $\mathbf R^3$.
• The cross-product.