Ciro Santilli $$Sponsor Ciro$$ 中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件 邓家贵、低端人口、西藏骚乱
🔗

# Bilinear map

| 🗖 nosplit | ↑ parent "Multilinear map" | words: 133
🔗
🔗
Linear map of two variables.
🔗
More formally, given 3 vector spaces X, Y, Z over a single field, a bilinear map is a function from: $$f:X×Y→Z (87)$$ that is linear on the first two arguments from X and Y, i.e.: $$f(a1​x1​​+a2​x2​​,y​)=a1​f(x1​​,y​)+a2​f(x2​​,y​) (88)$$ Note that the definition only makes sense if all three vector spaces are over the same field, because linearity can mix up each of them.
🔗
The most important example by far is the dot product from , which is more specifically also a symmetric bilinear form.
🔗
🔗

🔗