A n×n matrix A is an orthogonal matrix if A A^T = I, where A^T is the transpose of A and I is the identity matrix. In particular, an orthogonal matrix is always invertible, and A^(-1) = A^T. In component form, (a^(-1))_(i j) = a_(j i). This relation make orthogonal matrices particularly easy to compute with, since the transpose operation is much simpler than computing an inverse.
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