WOLFRAM|DEMONSTRATIONS PROJECT

Triangle Inequality for Functions

f(x)

2

x

x

cos(x)

sin(x)

g(x)

2

x

x

cos(x)

sin(x)

Choose functions

f(x)

and

g(x)

and use the two graphs to understand the triangle inequality. In the vector space of square integrable functions, the inner product of the functions

f

and

g

is

〈f,g〉=

1

∫

-1

f(x)g(x)dx

and the norm of

f

is

f=

〈f,f〉

.