High Quality Content by WIKIPEDIA articles! In mathematics, the orthogonal group of degree n over a field F (written as O(n,F)) is the group of n-by-n orthogonal matrices with entries from F, with the group operation that of matrix multiplication. More generally the orthogonal group of a non-singular quadratic form over F is the group of linear operators preserving the form (the above group O(n,F) is then the orthogonal group of the sum-of-n-squares quadratic form). The Cartan–Dieudonne theorem describes the structure of the orthogonal group.

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