What is a mathematical term for a non-rectangular matrix/array?

Question

In computer science, we can have a list of lists, and the sublists can have different lengths.

In math, is there a concept for such non-rectangular "matrix"? If I am correct, array and matrix are used for rectangular ones only.

Answer 1

Not really. Matrices are maps between spaces, where columns and rows are base vectors for their spaces. On them, a scalar product has to be definable - and this just works if one can exist in a space that the other "lives in". They therefore cannot be smaller or larger, therefore have to be the same length.

So no, not as a matrix. But you can define yourself a set of vectors. Questionable if you can define any deeper operations with them.

Answer 2

Given a ground set $X$ and an $n\in{\mathbb N}_{\geq1}$ a function ${\bf a}:\>[n]\to X$ is called an $n$-tuple and is presented in the form $(a_1,a_2,\ldots, a_n)$. A tuple is then an $n$-tuple for some $n\geq1$ – it's the same thing as what you call a list in your question. Now I have never seen a "tuple of tuples", but would be willing to consider a family of tuples, indexed by some index set $I$, which might again be a set of the form $[n]$. So you can speak of a family ${\cal F}=\bigl({\bf a}_\iota\bigr)_{\iota\in I}$