**Orthonormal basis sets - Kronecker delta function** The Kronecker delta function d

_{ij} = 0 if not i=j, and 1 if i=j.

A vector set V is said to be orthonormal if the scalar product of any two vectors is equal to the Kronecker delta function.

if {|i>}

_{N} is the basis set, for any vector |i> of that basis set there is a vector |j> that is also member of the basis set for which <i|j> = d

_{ij} It is always possible to choose any basis set and orthogonalize and normalize it

*a posteriori* The product of any two vectors

**a**.

**b** = a.b.cos(fi) where a and b are the magnitudes (lengths) of vectors

**a** and

**b** and where fi is the angle between the two vectors.

If the vectors are orthogonal the angle is 90 degrees and cos(fi) = 0

__See also:__ Scalar product of vectors

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1200341195 Orthonormal basis

http://en.wikipedia.org/wiki/Orthonormal_basis