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for vectors in . Compare this to the corresponding formula in by
by
for vectors in .
Norm and Distance in
By analogy with 3, we define the Euclidean norm (or Euclidean length) of a vector
and we define the Euclidean distance between the points and
EXAMPLE 6 Norm and Distance
If and , then
and
The complex vector space with norm and inner product defined above is called complex Euclidean n-space.
Exercise Set 10.4
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Let , , and . Find
1.
(a)
(b)
(c)
