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nLab > Latest Changes: Cauchy–Schwarz inequality

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 30th 2022

    Added a statement.

    diff, v2, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 30th 2022

    Added:

    Given a real or complex inner product space, we have

    |⟨u,v⟩|≤‖u‖⋅‖v‖.|\langle u,v\rangle|\le \|u\|\cdot\|v\|.

    Names

    Known as “Cauchy inequality”, “Cauchy–Schwarz inequality”, “Cauchy–Bouniakowsky–Schwarz” inequality.

    Proofs were published by Cauchy in 1821, Bouniakowsky in 1859, Hermann Schwarz in 1888.

    References

    !redirects Cauchy-Schwarz inequality !redirects Cauchy inequality

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 30th 2022

    added cross-link with Augustin Cauchy

    diff, v3, current

1 to 3 of 3

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