Let p 1 ( x ) = a + b x and p 2 ( x ) = c + d x be vectors in P 1 ( R ) . Determine a mapping 〈 p 1 , p 2 〉 that defines an inner product on P 1 ( R ) .
Let p 1 ( x ) = a + b x and p 2 ( x ) = c + d x be vectors in P 1 ( R ) . Determine a mapping 〈 p 1 , p 2 〉 that defines an inner product on P 1 ( R ) .
Solution Summary: The author explains the mapping langle,p_2rangle that defines a valid inner product.
Let
p
1
(
x
)
=
a
+
b
x
and
p
2
(
x
)
=
c
+
d
x
be vectors in
P
1
(
R
)
. Determine a mapping
〈
p
1
,
p
2
〉
that defines an inner product on
P
1
(
R
)
.
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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