bilinear form

《Advanced Linear Algebra》 · 第 259 页 · Chapter 11「Symmetric, Skew-Symmetric and Alternate Forms」

Definition Let $V$ be a vector space over $F$. A mapping $\langle\cdot,\cdot\rangle:V\times V\to F$ is called a bilinear form if it is linear in each coordinate, that is, if $\langle au+bv,w\rangle=a\langle u,w\rangle+b\langle v,w\rangle$ and $\langle u,av+bw\rangle=a\langle u,v\rangle+b\langle u,w\rangle$.