In this paper, we introduce the notion of almost pretopological vector spaces and present some examples of almost pretopological vector spaces. Almost pretopological vector spaces are defined by using ...

With some of the basic concepts of vector spaces in place, we now return to the abstraction of understanding the vector space as a collection of objects and algebraic operations that satisfy certain ...

We are now ready to define vector spaces. The idea is to observe that sets of column vectors, or row vectors, or more generally matrices of a given size, all come equipped with a notion of addition ...

"* zero vector $ 0 \\in V$\n", "5) vector addition: $a \\cdot (x+y) = a \\cdot x + a \\cdot y$\n", "6) real number addition: $(a + b) \\cdot x = a \\cdot x + b \\cdot ...