I understand that the special orthogonal group consists of matrices x such that [itex]x\cdot x=I[/itex] and [itex]detx=1[/itex] where I is the identity matrix and det x means the determinant of x. I get why the matrices following the rule [itex]x\cdot x=I[/itex] are matrices involved with rotations because they preserve the dot products of vectors. The part I dont get is why the matrices involved with rotation must have determinant 1.(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Why is the special orthogonal group considered the rotation group?

**Physics Forums | Science Articles, Homework Help, Discussion**