Orthonormal Basis and Completely Orthonormal System
Duan Li-fen
Abstract
Duan Li-fen
Abstract
On the foundation of the conception of orthonormal basis in finite dimensional Euclidean space,this paper provides the theory of completely orthonormal system in infinite dimensional Euclidean space.Thus it shows that completely orthonormal system in infinite dimensional Euclidean space is the natural generalizauion of orthonormal basis in finite dimensional Euclidean space.
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On the foundation of the conception of orthonormal basis in finite dimensional Euclidean space,this paper provides the theory of completely orthonormal system in infinite dimensional Euclidean space.Thus it shows that completely orthonormal system in infinite dimensional Euclidean space is the natural generalizauion of orthonormal basis in finite dimensional Euclidean space.
Key concepts: Orthonormal basis, Orthonormality, Basis (linear algebra), Euclidean space, Mathematics, Space (punctuation), Euclidean distance, Pure mathematics