Complete orthonormal set ↩

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created: 2021-12-13 23:07:35
modified: 2022-01-10 04:13:04

Let be an inner product space (a vector space equipped with an inner product) and .
is a complete orthonormal set if it is orthonormal and it is not a subset of any other orthonormal set that contains additional elements.

In this case, .1

We can see that orthonormal sets correspond to the Cartesian coordinate system.

Comments

That the orthonormal set is complete means obviously that no exists, with , which is orthogonal to the whole .

  1. Where is the dimension of
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