On Matroids and Linearly Independent Set Families

New families of matroids are constructed in this note. These new fami- lies are derived from the concept of linearly independent set family (LISF) introduced by Eicker and Ewald [Linear Algebra and its Applications 388 (2004) 173-191]. The proposed construction generalizes in a natural way the well known class of vectorial matroids over a ?field.