Is "linear algebra" restricted to the study of vector spaces on a Euclidean Space? If so, I think we should rename Definition:Vector (Euclidean Space) to Definition:Vector (Linear Algebra) and help firmly establish that category properly.
If "linear algebra" is considered as the study of all vector spaces, then Definition:Vector (Vector Spaces) should be renamed to Definition:Vector (Linear Algebra). (It is my belief that this is the case which holds, but I may be wrong.)
In that way the whole mess can be tidied up.
I originally envisaged two separate threads of thought using vectors: the abstract-algebraic version which treats elements of a general vector space, and the applied-mathematical one, the element of the 3-dimensional (etc.). The latter can be covered by a merging of Definition:Vector (Physics) with Definition:Vector (Euclidean Space), appropriately restructured. --prime mover 04:28, 20 May 2012 (EDT)
- I would say that (i.e., to me) Linear Algebra pertains to the study of finite-dimensional vector spaces. After that, I would be more tempted to call it Functional Analysis (so that FA encapsulates LA). --Lord_Farin 11:43, 20 May 2012 (EDT)