Gram-Schmidt process
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The Gram-Schmidt process is an algorithm for producing an orthonormal basis from a set of vectors that are not orthogonal.[1] These vectors are orthogonal in the sense that their inner product is for any two basis vectors <math>\vec{v}_i</math> and <math>\vec{v}_j</math> is:
- <math>
\langle \vec{v}_i|\vec{v}_j \rangle = \delta_{ij} </math>
where <math>\delta_{ij}</math> is the Kronecker delta, equal to 1 if i=j and 0 otherwise. They are then said to be orthonormal as the norm of any vector is 1: <math>||\vec{v}_i|| = 1</math>. It is used in quantum mechanics to create a basis of eigenfunctions to represent wavefunctions.[2]