Properties of Overcomplete and Nonorthogonal Basis Vectors

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Abstract
An alternative to the Schmidt procedure is presented for the orthogonalization of a set of functions or state vectors. The method is particularly simple and ideally suited to the eigenvalue problem in a space spanned by nonorthonormal, and even overcomplete, basis vectors. The method is applied to the solution of the equation of motion with a non‐unit‐metric matrix and to the problem of eliminating spurious (or any other) states from a given vector space.