# Orthonormal Vectors

A collection of vectors \(a_1, \cdots, a_k\) is orthogonal, or mutually orthogonal if \(a \perp b\) for any \(i\), \(j\) with \(i \neq j\), \(i\), \(j = 1, \cdots, k\). A collection of vectors \(a_1, \cdots, a_k\) is orthonormal if its orthogonal and \(||a_i|| = 1\) for \(i = 1, \cdots, k\). A vector of norm one is called normalized; dividing a vector by its norm is called normalizing it. …