Exercise
https://texercises.com/exercise/characteristic-polynomial-and-injectivity/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Let V be a vector space over K and T:Vrightarrow V a linear map. Then lambda in K is an eigenvalue of T iff the linear map T-lambda id_V is not injective.

Solution:
Proof. lambda textis an eigenvalue of T &iff exists neq vin V:Tvlambda v &iff exists neq vin V:Tv-lambda v &iff exists neq vin V:T-lambda id_Vv &iff textKerT-lambda id_Vneq &iff T-lambda id_V textis not injective.
Report An Error
You are on texercises.com.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!
Meta Information
\(\LaTeX\)-Code
Exercise:
Let V be a vector space over K and T:Vrightarrow V a linear map. Then lambda in K is an eigenvalue of T iff the linear map T-lambda id_V is not injective.

Solution:
Proof. lambda textis an eigenvalue of T &iff exists neq vin V:Tvlambda v &iff exists neq vin V:Tv-lambda v &iff exists neq vin V:T-lambda id_Vv &iff textKerT-lambda id_Vneq &iff T-lambda id_V textis not injective.
Contained in these collections:

Attributes & Decorations
Tags
characteristic polynomial, eigenvalue, eigenvector, eth, fs23, injective, lineare algebra, proof
Content image
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Proof
Creator rk
Decoration