Let x = ( 5 , 2 , 4 ) T and y = ( 3 , 3 , 2 ) T . Compute ‖ x − y ‖ 1 , ‖ x − y ‖ 2 , and ‖ x − y ‖ ∞ . Under which norm are the two vectors closest together? Under which norm are they farthest apart?
Let x = ( 5 , 2 , 4 ) T and y = ( 3 , 3 , 2 ) T . Compute ‖ x − y ‖ 1 , ‖ x − y ‖ 2 , and ‖ x − y ‖ ∞ . Under which norm are the two vectors closest together? Under which norm are they farthest apart?
Solution Summary: The author calculates the norms of two vectors closet together and farthest apart.
Let
x
=
(
5
,
2
,
4
)
T
and
y
=
(
3
,
3
,
2
)
T
.
Compute
‖
x
−
y
‖
1
,
‖
x
−
y
‖
2
,
and
‖
x
−
y
‖
∞
.
Under which norm are the two vectors closest together? Under which norm are they farthest apart?
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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