Exercise
https://texercises.com/exercise/dimension-of-homomorphisms/
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:
If VW are finite dimensional vector spaces then so it textHomVW and textdim HomVWtextdimV textdimW.

Solution:
Proof. Put n: textdimV m:textdimW. By the previous theorem we have textHomVWcong M_mtimes nK Longrightarrow textHomVW is finite dimensional and textdim HomVWtextdimM_mtimes nKm n.
Report An Error
You are on texercises.com.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!
Meta Information
\(\LaTeX\)-Code
Exercise:
If VW are finite dimensional vector spaces then so it textHomVW and textdim HomVWtextdimV textdimW.

Solution:
Proof. Put n: textdimV m:textdimW. By the previous theorem we have textHomVWcong M_mtimes nK Longrightarrow textHomVW is finite dimensional and textdim HomVWtextdimM_mtimes nKm n.
Contained in these collections

Similar exercises (48)
Title Creator Matched on
Subspaces and dimensions rk tags
Dimension and vector spaces rk tags
Dimension of quotient space rk tags
Dimension of the dual space rk tags
Group characteristics rk tags
more (43 more)
Attributes & Decorations
Tags
dimension, eth, hs22, lineare algebra, proof
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Proof
Decoration
Content image