# 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 $\pm 1$.