Get Math Help

GET TUTORING NEAR ME!

(800) 434-2582

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Home / Get Math Help

    Orthogonal Group

    Definition

    For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and taking inverses. Thinking of a matrix as given by n^2 coordinate functions, the set of matrices is identified with R^(n^2). The orthogonal matrices are the solutions to the n^2 equations A A^T = I, where I is the identity matrix, which are redundant. Only n(n + 1)/2 of these are independent, leaving n(n - 1)/2 "free variables." In fact, the orthogonal group is a smooth n(n - 1)/2-dimensional submanifold.

    Back to List | POWERED BY THE WOLFRAM LANGUAGE