Topic: Orthogonal Matrices and Isometries

Unitary Matrices and Complex Inner-Product Preservation

Rotation Matrices in R^2

Reflections Across Lines in R^2

Products, Inverses, and Powers of Orthogonal Matrices

Orthonormal Columns and the Equation Q^TQ = I

Orthogonal Changes of Coordinates in Orthonormal Bases

Mapping Vectors with Householder Reflections

Inner-Product and Norm Preservation by Orthogonal Matrices

Exact Tests for Orthogonality in Worked Matrix Examples

Equivalent Tests for Orthogonal Matrices