Ciro Santilli $£ Sponsor €¥ 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
Given a matrix with metric signature containing positive and negative entries, the indefinite orthogonal group is the set of all matrices that preserve the associated bilinear form, i.e.:
Note that if , we just have the standard dot product, and that subcase corresponds to the following definition of the orthogonal group: Section "The orthogonal group is the group of all matrices that preserve the dot product".
As shown at all indefinite orthogonal groups of matrices of equal metric signature are isomorphic, due to the Sylvester's law of inertia, only the metric signature of matters. E.g., if we take two different matrices with the same metric signature such as:
both produce isomorphic spaces. So it is customary to just always pick the matrix with only +1 and -1 as entries.


  1. Indefinite orthogonal group
  2. Lorentz group
  3. Poincaré group
  4. Important Lie group
  5. Lie group
  6. Differential geometry
  7. Geometry
  8. Area of mathematics
  9. Mathematics
  10. Ciro Santilli's Homepage