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... I think I would rate "array element" higher than
"matrix element".
I believe I have this prejudice because my first
encounter with the word "array" was (perhaps) in a programming
context where the first kind of array I encountered was a
one-dimensional array whereas my first encounter with the word
"matrix" was (perhaps) in a mathematics course where the first kind
of matrix that was referred to as a matrix was a two-dimensional
matrix.
A Google search on "scalar projection" indicates that some people
think that there are at least two kinds of projections of a vector
onto another vector. See, for instance,
<http://en.wikipedia.org/wiki/Dot_product> where a diagram caption
reads "|a|*cos(θ) is the scalar projection of a onto b".
This might
actually argue in favor of using the word "projection" for what some
folks call a "component vector" in that it would help folks learn
what a projection really is but it indicates that it is not
self-describing to everybody.
I like component vector because it is
self-describing; its name tells everyone that it is a vector.