For two- and three-dimensional vectors, the fundamental property of dot products,
A · B = |A||B| cos θ, implies that
| A · B | ≤ | A || B | . (2.3.44)
In this exercise, we generalize this to n-dimensional vectors and functions, in which case (2.3.44) is known as Schwarz’s inequality. [The names of Cauchy and Buniakovsky are also associated with (2.3.44).]
(a) Show that |A − γB|2 > 0 implies (2.3.44), where γ = A · B/B · B.
(b) Express the inequality using both
*(c) Generalize (2.3.44) to functions. [Hint: Let A · B mean the integral
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