Linear Algebra and Its Applications · Problem 7.2.18

Computations with Matrices — Gilbert Strang

Mathematics · vector-norms

Problem

The ``

\ell^1

norm'' is

\|x\|_1 = |x|_1 + \cdots + |x|_n

. The ``

\ell^\infty

norm'' is

\|x\|_\infty = \max|x_i|

. Compute

\|x\|

\|x\|_1

and

\|x\|_\infty

for the vectors

x = (1,1,1,1,1) \qquad \text{and} \qquad x = (.1,.7,.3,.4,.5).