Let L be a linear operator on a vector space V . Define L n , n ≥ 1 , recursively by L 1 = L L k + 1 ( v ) = L ( L k ( v ) ) for all v ∈ V Show that L n is a linear operator on V for each n ≥ 1
Let L be a linear operator on a vector space V . Define L n , n ≥ 1 , recursively by L 1 = L L k + 1 ( v ) = L ( L k ( v ) ) for all v ∈ V Show that L n is a linear operator on V for each n ≥ 1
Solution Summary: The author explains that Ln is a linear operator on V for each Nge 1.
Let L be a linear operator on a vector space V. Define
L
n
,
n
≥
1
, recursively by
L
1
=
L
L
k
+
1
(
v
)
=
L
(
L
k
(
v
)
)
for all
v
∈
V
Show that
L
n
is a linear operator on V for each
n
≥
1
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.
College Algebra with Modeling & Visualization (5th Edition)
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