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2. Finite-dimensional spaces
2.1 General results
All the above applies when H is a finite-dimensional vector space p on
. In this case, the terminology is clarified. A real pre-Hilbert space is called a Euclidean space, and a complex pre-Hilbert space is called a Hermitian space.
Schmidt's procedure, applied to any basis of H, shows that H admits an orthonormal basis
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Finite-dimensional spaces
Hilbert spaces
References
In Engineering Techniques
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