Inequality

The Cauchy-Schwartz inequality states for all vectors 𝐮,𝐯\mathbf{u}, \mathbf{v} of an inner product space (real vector space with inner product),

|⟨𝐮,𝐯⟩|2≤⟨𝐮,𝐮⟩⋅⟨𝐯,𝐯⟩\left|\langle \mathbf {u} ,\mathbf {v} \rangle \right|^{2}\leq \langle \mathbf {u} ,\mathbf {u} \rangle \cdot \langle \mathbf {v} ,\mathbf {v} \rangle

Notes

References

  1. https://en.wikipedia.org/wiki/Cauchy–Schwarz_inequality
  2. A. N. Kolmogorov and S. V. Fomin, Elements of the theory of functions and functional analysis, vol. 1, 2 vols. Graylock Press, 1961, p. 17.