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orthonormal set

An orthogonal set whose vectors also all have length 1.

A set \{\mathbf e_1,\dots,\mathbf e_k\} is orthonormal if it is pairwise orthogonal and every vector has unit length, \lVert\mathbf e_i\rVert=1. Any orthogonal set of nonzero vectors becomes orthonormal by normalizing each one. When an orthonormal set is a basis of a subspace, its coordinates are found by a single dot product per basis vector — no system to solve.

See also

orthogonal set unit vector orthogonal matrix Gram-Schmidt process
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