Orthogonal matrices

Overview

Orthogonal matrices are important for a number of reasons, both theoretical and practical. The n × n orthogonal matrices form a group under matrix multiplication, the orthogonal group denoted by O(n), which—with its subgroups—is widely used in mathematics and the physical sciences. For example, the point group of a molecule is a subgroup of O(3). Because floating point versions of orthogonal matrices have advantageous properties, they are key to many algorithms in numerical linear algebra, such as QR decomposition. As another example, with appropriate normalization the discrete cosine transform (used in MP3 compression) is represented by an orthogonal matrix.