Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Use the universal property of the tensor product to show that: given line maps T₁: V₁ → W₁ and T₂ : V₂ → W₂ we get a well defined linear map T₁ T2: V₁ V₂ → W₁ 0 W₂ with the property that (T₁ ® T₂) (v₁ 0 V₂) = T₁(v₁) | T₂(v₂) for all v₁ € V₁, V₂ € V₂

Use the universal property of the tensor product to show that: given line maps T₁: V₁ → W₁ and T₂ : V₂ → W₂ we get a well defined linear map T₁ T2: V₁ V₂ → W₁ 0 W₂ with the property that (T₁ ® T₂) (v₁ 0 V₂) = T₁(v₁) | T₂(v₂) for all v₁ € V₁, V₂ € V₂

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

how can i use the universal property of the tensor product to solve this? Should I construct a map? bilinear map? i need some explanation with this. Thank you

Use the universal property of the tensor product to show that: given linear maps T₁: V₁ → W₁ and T2 : V₂ → W₂ we get a well defined linear map T₁ T2 : V₁0 V₂ → W₁ 0 W₂ with the property that (T₁ T₂) (V₁ 0 V₂) = T₁ (v₁) ❀ T₂(v₂) for all v₁ € V₁, V₂ € V₂
Transcribed Image Text:Use the universal property of the tensor product to show that: given linear maps T₁: V₁ → W₁ and T2 : V₂ → W₂ we get a well defined linear map T₁ T2 : V₁0 V₂ → W₁ 0 W₂ with the property that (T₁ T₂) (V₁ 0 V₂) = T₁ (v₁) ❀ T₂(v₂) for all v₁ € V₁, V₂ € V₂
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS