bilinear

defined by the vector space V on the coefficient body F bilinear format B: V × V → F is

• $B(u+v,w)=B(u,w)+B(v,w)$
• $B(u,v+w)=B(u,v)+B(u,w)$
• $B(\lambda u,v)=B(u,\lambda v)=\lambda B(u,v)$ Satisfy the following.

As a concrete example, consider the inner product $B(u,v)=u\cdot v$, which satisfies the above conditions.

relevance - bilinear model - log-bilinear model - bilinearity

This page is auto-translated from /nishio/双線形 using DeepL. If you looks something interesting but the auto-translated English is not good enough to understand it, feel free to let me know at @nishio_en. I’m very happy to spread my thought to non-Japanese readers.