In mathematical texts matrices are generally given in an abstract representation
with symbolic dimensions, using ellipses to denote sequences of elements of
variable length. These representations essentially describe whole classes of
matrices, encompassing a range of concrete dimensions and for special classes
such as Vandermonde matrices, Toeplitz matrices, etc. a range of properties is
known which can be exploited for efficient computations. Thus when presented
with a fully instantiated matrix, where every element is a symbolic or numerical
value, one can ask the question whether this matrix belongs to a particular
class of matrices in order to exploit its respective properties.

In previous work we have developed a parsing procedure for extracting the
semantic of abstract matrix expressions involving ellipses and symbolic
dimensions together with a computational theory for arithmetic on abstract
matrices.  In this talk I shall now present how elements of the parsing
procedure can be exploited in order to abstract matrices to determine which
particular class they belong to. In particular, anti-unification, 2-d region
finding and graph analysis can be employed in a two stage procedure that firstly
abstracts a matrix by replacing sequences and regions of elements with
elliptical constructs and secondly generalises the result by introducing
symbolic dimensions. I shall also discuss some of the ambiguities arising from
generalisation and present some strategies how to deal with them.

This is joint work with Randa Almomen and Alan Sexton.