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https://texercises.com/exercise/representation-and-invertible-matrix/
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Exercise:
Let T:Vlongrightarrow W be an isomorphism between two finite dimensional vector spaces. Let mathcalBC be bases for VW. Then T_mathcalC^mathcalB is an invertible matrix and T^-_mathcalB^mathcalCleftT_mathcalC^mathcalBright^-.

Solution:
Proof. Let n:textdimVtextdimW. We have T^-_mathcalB^mathcalC T_mathcalC^mathcalBid_V_mathcalB^mathcalBI_n T_mathcalC^mathcalB T^-_mathcalB^mathcalCid_W_mathcalC^mathcalCI_n
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Exercise:
Let T:Vlongrightarrow W be an isomorphism between two finite dimensional vector spaces. Let mathcalBC be bases for VW. Then T_mathcalC^mathcalB is an invertible matrix and T^-_mathcalB^mathcalCleftT_mathcalC^mathcalBright^-.

Solution:
Proof. Let n:textdimVtextdimW. We have T^-_mathcalB^mathcalC T_mathcalC^mathcalBid_V_mathcalB^mathcalBI_n T_mathcalC^mathcalB T^-_mathcalB^mathcalCid_W_mathcalC^mathcalCI_n
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eth, hs22, lineare algebra, matrices, proof, vector space
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(3, default)
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ENG (English)
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Proof
Creator rk
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