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I have a basic question: if you have a linear combination of two vectors u, v where u = $ \begin{bmatrix} a_1 \\ \vdots \\ a_n \ \end{bmatrix} $ and v = $ \begin{bmatrix} w_1 \\ \vdots \\ w_n \ \end{bmatrix} $ and where $\ w_1+w_2+\cdots+w_n = 1 $ and $\ w_1, w_2, \ldots ,w_n $ are all positive real numbers and $\ a_1, a_2, \ldots ,a_n $ are all positive integers.

My question: Does $ u \cdot v $ converge to say a real number A no matter the size of $ n $?

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  • $\begingroup$ If the vector space has finite dimension, any product $u\cdot v$ will converge. $\endgroup$ – jobe Apr 5 '18 at 14:27
  • $\begingroup$ What do you mean by "converge" here? What is the sequence? $u\cdot v$ is just a real number by definition. $\endgroup$ – wgrenard Apr 5 '18 at 15:08
  • $\begingroup$ So really does there exist a limit A for u⋅v as n goes to infinity? $\endgroup$ – Se7venn Apr 5 '18 at 20:57

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