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Orthogonal Basis -- from Wolfram MathWorld

  • ️Weisstein, Eric W.

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An orthogonal basis of vectors is a set of vectors {x_j} that satisfy

x_jx_k=C_(jk)delta_(jk)

and

x^mux_nu=C_nu^mudelta_nu^mu,

where C_(jk), C_nu^mu are constants (not necessarily equal to 1), delta_(jk) 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.