Inner product space

A (real or complex) vector space together with an inner product:

In the case of C it is called a Hermitian inner product. In the case of R is a scalar product or dot product.

If the associated norm gives rise to a topology such that the space is Cauchy complete then it is called a Hilbert space

Identities

Orthonormal basis

They are basis of the vector space which satisfy ei,ej=δij.

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es


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