Basis (Hilbert Space)/Examples/Real Vector Space

Example of Basis (Hilbert Space)

Let $\R^d$ be the real vector space with $d$ dimensions.

Let $e_1, \ldots, e_d$ be the standard basis.

Then $\set{ e_1, \ldots, e_d }$ is a basis for the Hilbert space $\R^d$.

Proof

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Sources

• 1990: John B. Conway: A Course in Functional Analysis (2nd ed.) ... (previous) ... (next): $\text{I}$ Hilbert Spaces: $\S 4.$ Orthonormal Sets of Vectors and Bases: Example $4.4$