An orthogonal basis of vectors is a set of vectors {x_j} that satisfy x_j x_k = C_(j k) δ_(j k) and x^μ x_ν = C_ν^μ δ_ν^μ, where C_(j k), C_ν^μ are constants (not necessarily equal to 1), δ_(j k) is the Kronecker delta, and Einstein summation has been used. If the constants are all equal to 1, then the set of vectors is called an orthonormal basis.

basis | operator spectrum | orthogonal vectors | orthonormal basis