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I have two column vecotors $A$ and $B$. I multiply all the corresponding elements of $A$ with the corresponding elements of $B$ and call the result $x$. Now I sum all the elements of $x$ and subtract the result from $B$ (from what I presume is all the elements of $B$). This result is in turn is multipled with $A$ again to give the final answer of $0$. Why is this the case? Is there a particular name to this property of vectors?

Below is a MATLAB exercise screenshot of where I am getting this particular question. $A$ is x' and $B$ is y'

enter image description here

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  • $\begingroup$ If any mod sees this, please could you actually post the picture from the link, into the question ? I do not have enough reputation for this! $\endgroup$
    – SDG
    Nov 26, 2015 at 18:26
  • $\begingroup$ I'm sure that you have something in your notes or textbook about the dot product.... $\endgroup$
    – horchler
    Nov 26, 2015 at 20:16

1 Answer 1

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The actions described in steps (d) and (e) are the definition of "*" in step (f)$:

$$\begin{bmatrix}x_1&x_2&\cdots&x_n\end{bmatrix}*\begin{bmatrix}y_1\\y_2\\\vdots\\y_n\end{bmatrix} := [x_1y_1 + x_2y_2 + \cdots + x_ny_n]$$

That your difference was $0$ simply tells you that you didn't goof up, and neither did the machine.

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