1) Consider V R3 with standard basis e₁, C2, C3. phism VOV* → · L(V, V) ≈ M3×3 (R) and that we denote the linear map we get under this isomorphism just by 004 for ve V, pe V*. Let y(y) = x + z - ()- we have an isomor- (a) (b) (c) Find the linear map (ie matrix) associated to the tensor e₂ ❀ Find the linear map (ie matrix) associated to the tensor e₁ Find the linear map (ie matrix) associated to the tensor (2e₁ + 3e2)
1) Consider V R3 with standard basis e₁, C2, C3. phism VOV* → · L(V, V) ≈ M3×3 (R) and that we denote the linear map we get under this isomorphism just by 004 for ve V, pe V*. Let y(y) = x + z - ()- we have an isomor- (a) (b) (c) Find the linear map (ie matrix) associated to the tensor e₂ ❀ Find the linear map (ie matrix) associated to the tensor e₁ Find the linear map (ie matrix) associated to the tensor (2e₁ + 3e2)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
Transcribed Image Text:1) Consider V
phism
=
R3 with standard basis e₁, C2, C3.
(a)
(b)
(c)
~ M3x3 (R)
and that we denote the linear map we get under this isomorphism just by
004
V&V* ·L(V, V) ~
for v € V, y € V*. Let y(y) = x + Z
(-)
we have an isomor-
Find the linear map (ie matrix) associated to the tensor €2
4
Find the linear map (ie matrix) associated to the tensor e₁
Find the linear map (ie matrix) associated to the tensor (2e₁ +3e₂) |
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