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Using a lowercase letter for scalar projection is quite common. I added a new section Vector projection#Notation in which I explained this notation. See also this text copied from Euclidean vector:
From Euclidean vector |
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Another way to represent a vector in n-dimensions is to introduce the standard basis vectors. For instance, in three dimensions, there are three of them:
These have the intuitive interpretation as vectors of unit length pointing up the x, y, and z axis of a Cartesian coordinate system, respectively. In terms of these, any vector a in can be expressed in the form: where a1, a2, a3 are called the vector components (or vector projections) of a on the basis vectors or, equivalently, on the corresponding Cartesian axes x, y, and z (see figure), while a1, a2, a3 are the respective scalar components (or scalar projections). In introductory physics textbooks, the standard basis vectors are often instead denoted (or , in which the hat symbol ^ typically denotes unit vectors). In this case, the scalar and vector components are denoted respectively ax, ay, az, and ax, ay, az (note the difference in boldface). Thus, |
Paolo.dL (talk) 16:09, 24 April 2013 (UTC)
Essentially all of the content in Scalar projection is already in this article, so there's no need to have duplicate information. So a merge makes sense to me. Mark M (talk) 17:38, 24 April 2013 (UTC)
I removed an erroneous note about performance (https://en.wikipedia.org/w/index.php?title=Vector_projection&type=revision&diff=857678811&oldid=800732724). The note claimed the latter method was faster, when in reality it depends on the platform, implementation, and context (but the former is probably faster). The normalization is likely to boil down to multiplication by a reciprocal square root, which is quite fast on modern CPUs. However, counting operations is not a very good way to reason about performance, so even that doesn't tell the whole story. If anyone wants to add performance-related information back into the article, please make sure are aware of all the relevant details first, to avoid giving bad advice. 72.161.48.132 (talk) 09:09, 2 September 2018 (UTC)
I was unfamiliar with the hat notation for normalized vectors. To me, hats are more commonly used for estimated values (e.g. mean quantities, statistical estimators, or best-fit parameters). While I acknowledge that using hats are used for normalized vectors in some fields/articles, I feel like for this article it is unnecessary. I propose that be replaced with . It won't complicate the equations much, and then we can remove the two places where the hat notation is described. --Quantum7 09:04, 9 May 2019 (UTC)
wide overlap; possibly renaming to Vector and scalar projection. fgnievinski (talk) 05:35, 4 September 2023 (UTC)