6.0 Cauchy-Schwarz Inequality

  Inequalities

    6.0 Cauchy-Schwarz Inequality

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6.0 Cauchy-Schwarz InequalityIf ${a_1},{a_2},...,{a_n}$ and ${b_1},{b_2},...,{b_n}$ are any real numbers such that $${({a_1}{b_1} + {a_2}{b_2} + ... + {a_n}{b_n})^2} \leqslant ({a_1}^2 + {a_2}^2 + ... + {a_n}^2) \times ({b_1}^2 + {b_2}^2 + ... + {b_n}^2)$$ Equality holds if $$\frac{{{a_1}}}{{{b_1}}} = \frac{{{a_2}}}{{{b_2}}} = ... = \frac{{{a_n}}}{{{b_n}}}$$