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 . Moreover, given this basis, the application :
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Finite-dimensional spaces
Hilbert spaces
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