An algorithm for converting any basis into an orthonormal basis.

Representing the change of basis in matrix form leads to the QR-Factorization: M = QR, which is unique.

A linear transformation T is called orthogonal if it preserves the length of vectors. The matrix used to obtain the orthogonal transformation is called an orthogonal matrix.

Interchange the rows and columns of a matrix.

A square matrix A is symmetric if the transpose of A is equal to A.

A square matrix A is skew-symmetric if the transpose of A is equal to -A.

- Section 5.2 - 3, 11, 17, 25, 31, 35
- Section 5.3 - 1, 3, 5, 7, 11, 15, 19, 25, 33
- Section 5.4 - 1, 19, 21, 31, 36