Paper 3, Section II, D

Groups | Part IA, 2019

What is the orthogonal group O(n)\mathrm{O}(n) ? What is the special orthogonal group SO(n)?\mathrm{SO}(n) ?

Show that every element of SO(3)\mathrm{SO}(3) has an eigenvector with eigenvalue 1.1 .

Is it true that every element of O(3)\mathrm{O}(3) is either a rotation or a reflection? Justify your answer.

Typos? Please submit corrections to this page on GitHub.