Today I Learned

Some of the things I've learned every day since Oct 10, 2016

214: Orthogonal Matrices

In linear algebra, an orthogonal matrix is a square matrix A such that

AT^T = A^T A = I.

Equivalently, the rows and columns of A are, respectively, orthonormal vectors: vectors which are all unit length and orthogonal to one another.

Also equivalently, A^{-1} = A^T.

A fun fact about orthogonal matrices is that their determinants are always \pm 1.

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