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Exercise:
Ase VK^n and let phi:K^nrightarrow K be a functional. Then exists ! Aa_...a_nin M_times nK s.t. phivAv forall vin K^n.

Solution:
Proof. Indeed let e_...e_n be the standard basis for K^n and define a_phie_...a_nphie_n. Let vleftarrayc v_ vdots v_n arrayrightin K^n. Then phivphileftarrayc v_ vdots v_n arrayright phi v_ e_+...+v_n e_n v_phie_+...+v_nphie_n v_a_+...+v_na_n A v
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Exercise:
Ase VK^n and let phi:K^nrightarrow K be a functional. Then exists ! Aa_...a_nin M_times nK s.t. phivAv forall vin K^n.

Solution:
Proof. Indeed let e_...e_n be the standard basis for K^n and define a_phie_...a_nphie_n. Let vleftarrayc v_ vdots v_n arrayrightin K^n. Then phivphileftarrayc v_ vdots v_n arrayright phi v_ e_+...+v_n e_n v_phie_+...+v_nphie_n v_a_+...+v_na_n A v
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dual space, eth, fs23, inner product, lineare algebra, proof
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(3, default)
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0 (default)
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ENG (English)
Type
Proof
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