MathLiveCauchy–Schwarz inequality
It bounds the absolute value of the inner product of two vectors by the product of their norms, so the squared inner product never exceeds the product of the squared norms. It is used throughout linear algebra, analysis and probability to prove other inequalities and bound sums or integrals.
|\langle \mathbf{u},\mathbf{v}\rangle|^2 \leq \langle \mathbf{u},\mathbf{u}\rangle \cdot \langle \mathbf{v},\mathbf{v}\rangleWhat the symbols mean
| a vector in an inner product space | |
| a vector in the same inner product space | |
| the inner product of u and v |
About this formula
- FieldMathematics
- TopicInequalities
- LevelUniversity
- Also calledCauchy–Bunyakovsky–Schwarz inequality, Cauchy–Schwarz–Bunyakovsky inequality, Cauchy Schwarz inequality, inner product inequality, vector inequality absolute value of inner product, Bunyakovsky inequality
- SourceWikidata Q190546
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