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https://texercises.com/exercise/dimension-of-homomorphisms/
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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.
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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.
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dimension, eth, hs22, lineare algebra, proof
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ENG (English)
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