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Exercise:
Let VW be finite dimensional inner product spaces and T:Vrightarrow W a linear map. Let mathcalBe_...e_n be an orthonormal basis for V and mathcalCf_...f_m an orthonormal basis for W. Then: T^*_mathcalB^mathcalCleftoverlineT_mathcalC^mathcalBright^T leftT_mathcalC^mathcalBright^*

Solution:
Proof. Write Aa_ij_leq ileq m leq jleq nT_mathcalC^mathcalB and Bb_ij_leq ileq n leq jleq mT^*_mathcalB^mathcalC We have: b_ijlangle T^*f_je_irangle overlinelangle e_i T^*f_jrangle overlinelangle Te_i f_jrangle overlinea_ij &Longrightarrow BoverlineA^TA^*
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Exercise:
Let VW be finite dimensional inner product spaces and T:Vrightarrow W a linear map. Let mathcalBe_...e_n be an orthonormal basis for V and mathcalCf_...f_m an orthonormal basis for W. Then: T^*_mathcalB^mathcalCleftoverlineT_mathcalC^mathcalBright^T leftT_mathcalC^mathcalBright^*

Solution:
Proof. Write Aa_ij_leq ileq m leq jleq nT_mathcalC^mathcalB and Bb_ij_leq ileq n leq jleq mT^*_mathcalB^mathcalC We have: b_ijlangle T^*f_je_irangle overlinelangle e_i T^*f_jrangle overlinelangle Te_i f_jrangle overlinea_ij &Longrightarrow BoverlineA^TA^*
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eth, fs23, lineare algebra, matrix, proof
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(3, default)
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ENG (English)
Type
Proof
Creator rk
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