Bilinearity
= Bilinearity
A map $B:V\times W\to Z$ between <vector spaces> is bilinear when it is <linear> in either argument with the other held fixed. A scalar-valued <bilinear form> is the case $V=W$ and $Z$ is the scalar field. Checking <bilinearity> is one of the algebraic steps in verifying a real <inner product>; being a <symmetric bilinear form> and having positive squared <norm> impose further conditions.