[Merged by Bors] - feat(analysis/inner_product/pi_L2): a finite orthonormal family is a basis of its span #15481
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Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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| /-- Any finite subset of a orthonormal family is an `orthonormal_basis` for its span. -/ | ||
| protected def span {v' : ι' → E} (h : orthonormal 𝕜 v') (s : finset ι') : | ||
| orthonormal_basis s 𝕜 (span 𝕜 (s.image v' : set E)) := | ||
| let |
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For consistency, could you write the proof in the same way as in basis.span, using orthonormal_basis.mk?
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…basis of its span (#15481) We actually prove this for finite sub-families of a generic orthonormal basis because this is easier to use in practice
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…basis of its span (leanprover-community#15481) We actually prove this for finite sub-families of a generic orthonormal basis because this is easier to use in practice
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…basis of its span (#15481) We actually prove this for finite sub-families of a generic orthonormal basis because this is easier to use in practice
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…basis of its span (#15481) We actually prove this for finite sub-families of a generic orthonormal basis because this is easier to use in practice
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We actually prove this for finite sub-families of a generic orthonormal basis because this is easier to use in practice
linear_equiv.of_eqas alinear_isometry_equiv#15471