Is it possible to project vector onto another vector that has different length ?

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Sarah A 2018-7-18

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评论： Sarah A 2018-7-21

Hello,

Is it possible to project vector (a) onto another vector (b) that has different length? for example, let a is a vector of 51 element and b is 90 element.

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Sarah A 2018-7-18

yes as in : •Wiki: vector projection

Jan 2018-7-19

@Sarah A: This definition from WikiPedia works only, if the vectors have the same length. So it is still not clear, what you want to achieve.

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Answer 1

Jan 2018-7-18

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在 MATLAB Online 中打开

A projection between vectors of different sizes is not mathematically defined. So it depends on what you need:

a = [a1, a2, a3]
b = [b1, b2, b3, b4, b5]

Then perhaps you want:

c = a1 * b1 + a2 * b2 + a3 * b3
c = a1 * b1 + a2 * b2 + a3 * b3 + b4 + b5
c = a1 * b3 + a2 * b4 + a3 * b5

I have not seen any mathematical problem in the last 30 years, in which such an operation is required. Please post the context of the problem, because I assume, that the need for this operation is a misunderstanding.

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Sarah A 2018-7-21

Thank you for answering. Yes I still working on my idea and if I have more details of what I am going to do I will comment here.

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Answer 2

Constantino Carlos Reyes-Aldasoro 2018-7-18

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As mentioned previously, we would need a bit more context to be able to provide more guidance. I guess that what you want to do is the dot product of two vectors, say A and B, so that you can see the projection of one over another and thus you would have two vectors with the same orientation, one is not modified and the second will have a different magnitude due to the projection, if they had the same orientation the magnitude is not changed, but if they were at 90 degrees of each other, the magnitude of the projection would be zero, that is, they are orthogonal to each other. Check wikipedia for dot product:

https://en.wikipedia.org/wiki/Dot_product

and the dot product help for Matlab

https://uk.mathworks.com/help/matlab/ref/dot.html

If you still have doubts after reading these, let us know.

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Matt J 2018-7-18

编辑：Matt J 2018-7-18

You tell us. What is the result supposed to represent? What are the inputs supposed to represent? Can we assume the representation of a in 5D is [a1,a2,a3,0,0] ?

Constantino Carlos Reyes-Aldasoro 2018-7-19