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In mathematics, one can project vector A onto another vector B, and the result vector P is called vector projection.

There's also related term, "vector rejection" defined by R = A - P where R denotes vector rejection.

You can find the exact definitions from wikipedia: https://en.wikipedia.org/wiki/Vector_projection

Anyway, I wonder I may say "reject a vector" in the same manner of "project a vector".

I've googled "reject a vector" but what all I could find was 'reject' in other usage(mainly refuse something).

Is it okay to say 'reject a vector' as a mathematical operation to get a vector rejection?

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  • Never heard it. My guess would be that while "to project onto a vector" is meaningful in the sense that it matches the usual meaning of the verb "to project", "to reject a vector" is problematic because reject has a very different meaning in everyday English. Google finds a number of papers where vectors are rejected but in the sense that they are not accepted (mostly in the context of vectors of random numbers). Mathematicians like to be precise, so may avoid "to reject".
    – painfulenglish
    Commented Apr 28, 2018 at 9:16
  • Whether you can "legally" use the term is up to the mathematicians -- they set their own linguistic rules.
    – Hot Licks
    Commented Apr 28, 2018 at 12:30
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    I'm voting to close this question as off-topic because it belongs on Maths SE; as Hot Licks says, 'they [mathematicians etc] set up their own rules', so usages can be non-standard and yet still totally acceptable within that domain.
    – Edwin Ashworth
    Commented Apr 28, 2018 at 14:01

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To "reject" a vector is uncommon, but so is "project" a vector. I went through the vector projection article and found "project" only once. In all other cases the term is used to find the projection of a vector onto another vector. The reason you can't find results for it is because:

  1. Rejection is less common an operation than projection.
  2. The verb is less commonly used than the noun in any case.

I have found the term being used at this Math Exchange question and in the Wikipedia Rejection disambiguation page

Rejection, or the verb reject, may refer to: In mathematics, the rejection of a vector a from a vector b is the component of a perpendicular to b, as opposed to its projection, which is parallel to b.

So it's rather uncommon but there's no reason you can't use it. Note though that unlike in your title, you don't reject a vector onto another vector, you reject a vector off from another vector. The caption in Wikipedia for the following image is:

Projection of a on b (a1), and rejection of a from b (a2).

enter image description here

Vector A has been projected onto vector b, which results in vector a1. By rejecting a OFF FROM vector B will give you vector a2 as a result. To avoid confusion you should make sure you mention which vector you're rejecting another vector off from, and even better, to say that you're performing the rejection of vector A OFF FROM vector B.

Though really, you should probably ask this on the Math SE site.

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  • Why do you recommend using the preposition "off", when Wikipedia uses "from"? They don't always mean the same thing, either in everyday speech or in technical English.
    – Peter Shor
    Commented Apr 28, 2018 at 11:20
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    @PeterShow This is why I recommended the OP ask at Math SE, because I'm not that into this. The way I saw it in my mind was "off" but you're right that the terminology is "from". I'll change.
    – Zebrafish
    Commented Apr 28, 2018 at 11:25
  • Since there are tons of people forced to use English even though they are good at including me, I thought that only few usage examples which can be found on internet does not mean it is correct. I wanted to ask for an opinion from who is good at English. But, as you said it's maybe too technical term. I'll ask on Math SE again. Thank you.
    – slyx
    Commented Apr 28, 2018 at 11:53
  • In my experience, "project" as a verb is actually quite commonly used in the context of quantum mechanics (where the vectors are infinite-dimensional). I'm also not sure the wikipedia article is a statistically relevant sample to infer if verbs are used or not.
    – painfulenglish
    Commented Apr 28, 2018 at 11:59
  • Oops, typo in previous comment. 'even though they are good at including me' should be 'even though they are NOT good at English including me'. @painfulenglish Yes, I'm very familiar with projecting a vector onto other vectors mainly onto other bases.
    – slyx
    Commented Apr 28, 2018 at 12:19
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I think it depends on whether your readers will understand you. Most people don't know of "vector rejection".

However, if your readers do, or if you define the term, as you did in the question, you could say, for example,

Finally, we reject X on Y to obtain the answer.

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