Bilinear form/Vector space/Definition

Let ${\displaystyle {}V}$ be a vector space over the field ${\displaystyle {}K}$. The set of all bilinear forms on ${\displaystyle {}V}$, endowed with pointwise addition and scalar multiplication, is called the vector space of bilinear forms. It is denoted by ${\displaystyle {}\operatorname {Bilin} _{}{\left(V\right)}}$.