In ℝ n with inner product 〈 x , y 〉 = x T y Derive a formula for the distance between two vectors x = ( x 1 , ... , x n ) T and y = ( y 1 , ... , y n ) T .
In ℝ n with inner product 〈 x , y 〉 = x T y Derive a formula for the distance between two vectors x = ( x 1 , ... , x n ) T and y = ( y 1 , ... , y n ) T .
Solution Summary: The author explains how to obtain a formula for the distance between the two vectors x and y in an inner product space.
In
ℝ
n
with inner product
〈
x
,
y
〉
=
x
T
y
Derive a formula for the distance between two vectors
x
=
(
x
1
,
...
,
x
n
)
T
and
y
=
(
y
1
,
...
,
y
n
)
T
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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