Abstract . A  long-standing problem in linear algebra is the construction of linear spaces of constant rank, whose origins are to be sought in the work of Kronecker and Weierstrass, giving us classical examples. We will see that, under mild assumptions, these matrices are always associated to a syzygy bundle

that fits in a (partially linear) resolution. Furthermore, our construction provides a new perspective which unifies the ones used in the examples known in literature and allows to build new ones, as well as to list all indecomposable matrices of constant rank up to 7.

This is an ongoing work with Rosa Maria Miró-Roig.