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
🔗

# The orthogonal group is the group of all matrices that preserve the dot product

| nosplit | ↑ parent "Definition of the orthogonal group" | words: 72 | descendant words: 244 | descendants: 1
🔗
When viewed as matrices, it is the group of all matrices that preserve the dot product, i.e.: $$O(n)=O∈M(n)∣∀x,y,xTy=(Ox)T(Oy) (197)$$ This implies that it also preserves important geometric notions such as norm and angles.
🔗
This is perhaps the best "default definition".
🔗

🔗