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So here is a theoretical question. Let L1 and L2 be linear transformation from a vector space V into Vector space W. Let {v1,v2,....,vn} be a basis for V. Show that if L1(vi)=L2(vi) for i=1,2,....,n then
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Jul 22, 2017
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So here is a theoretical question. Let L1 and L2 be linear transformation from a vector space V into Vector space W. Let {v1,v2,....,vn} be a basis for V. Show that if L1(vi)=L2(vi) for i=1,2,....,n then L1(v)=L2(v) for any v in V. ...?
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Ed Ayers
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if v belongs to V, then we can find scalars a1,a2,...,an, such that v=a1*v1+a2*v2+...+an*vn, L1(v)=L1(a1*v1+a2*v2+...+an*vn) =a1*L1(v1)+a2*L1(v2)+...+an*L1(vn) =a1*L2(v1)+a2*L2(v2)+...+an*L2(vn) =L2(a1*v1+a2*v2+...+an*vn) =L2(v)
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Jul 27, 2017
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