Cauchy–Schwarz Inequality

The Cauchy–Schwarz inequality is part of the Vectors topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-02). This subtopic proves and uses the Cauchy–Schwarz inequality for vectors, \(|\mathbf{a}\cdot\mathbf{b}| \le |\mathbf{a}||\mathbf{b}|\), which bounds the dot product of two vectors by the product of their magnitudes.

Students and teachers will cover how to prove the inequality using the scalar product and how to apply it to establish further results and bounds — a neat link between the dot product and inequalities in the HSC Extension 2 course.