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Orthogonal Basis


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.


See also

Basis, Operator Spectrum, Orthogonal Vectors, Orthonormal Basis

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Cite this as:

Weisstein, Eric W. "Orthogonal Basis." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OrthogonalBasis.html

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