I didn't mention the term "matrix". I think it has a much more complex story with respect to common use by "programmers" along with vector. Since linear algebra is such a commonly taught subject there are lots of people with practical working knowledge of matrices. If you don't have the geometric or abstract algebraic perspective here then matrix is almost certainly "2d-array" at first blush, but you'll also admit that there's a sort of non-trivial relationship between these "matrices" and size-conformant "vectors" (1d-arrays) and another one between two size-conformant matrices. This distinction is made from time to time [0][1].
Finally, of course, a matrix is a special case of a tensor. Tensor is such a broader topic that it becomes more and more difficult to talk about it without its geometric underpinnings. This is what I was writing about above.
[0] Is a black-and-white image a matrix? I'd imagine a lot of people would have a bit of a tough time saying yes directly---and for good reason. But there's also a reasonable argument for pretending like it is, and even reasonable arguments for turning it into one!
[1] Numpy distinguishes between nd-arrays and matrices exactly right in that matrices are 2d-arrays only and are imbued with multiplication as composition of maps. In practice, many people I know who are Numpy users just think of matrix as a convenient way to overload *, though.
Finally, of course, a matrix is a special case of a tensor. Tensor is such a broader topic that it becomes more and more difficult to talk about it without its geometric underpinnings. This is what I was writing about above.
[0] Is a black-and-white image a matrix? I'd imagine a lot of people would have a bit of a tough time saying yes directly---and for good reason. But there's also a reasonable argument for pretending like it is, and even reasonable arguments for turning it into one!
[1] Numpy distinguishes between nd-arrays and matrices exactly right in that matrices are 2d-arrays only and are imbued with multiplication as composition of maps. In practice, many people I know who are Numpy users just think of matrix as a convenient way to overload *, though.