If $sum_{i=1}^vu_iotimes v_i =0$ then $v_i=0$ for all $i=1,cdots, n$
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Let $U$ , $V$ be $K$ -vector spaces. Let $u_1,cdots, u_nin U$ be linear independent vectors and $v_1,cdots, v_nin V$ arbitrary vectors. Show that if $sum_{i=1}^vu_iotimes v_i =0$ then $v_i=0$ for all $i=1,cdots, n$ I can obviously show the converse, but it does not suffice. I tried to find the answer here but I couldn't. It seems simple but I don't know how to begin
linear-algebra
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asked Nov 17 at 18:07
Guerlando OCs
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