Category:Orthonormal Bases of Vector Spaces
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This category contains results about Orthonormal Bases of Vector Spaces.
Definitions specific to this category can be found in Definitions/Orthonormal Bases of Vector Spaces.
Let $\struct {V, \norm {\, \cdot \,} }$ be a normed vector space.
Let $\BB = \tuple {\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n}$ be a basis of $\struct {V, \norm {\, \cdot \,} }$.
Then $\BB$ is an orthonormal basis of $\struct {V, \norm {\, \cdot \,} }$ if and only if:
- $(1): \quad \tuple {\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n}$ is an orthogonal basis of $V$
- $(2): \quad \norm {\mathbf e_1} = \norm {\mathbf e_2} = \cdots = \norm {\mathbf e_n} = 1$
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