Linear Algebra

This work grew out of my study of families of bilinear forms which, in a natural way, determine vector spaces of matrices. If one stipulates that every matrix in the space has rank at most k then one can often prove strong properties of the space. It is easy to handle the rank 1 case (to within a natural equivalence) they consist of row vectors or column vectors. At rank 2 one gets an unusual example (essentially unique) of the 3-dimensional space of all 3x3 skew-symmetric matrices. For rank 3 the problem is harder but still controllable. So far as I know higher rank spaces have not been classified.

Papers on linear algebra

  1. Spaces of matrices of bounded rank, Quart. J. Math. 29 (1978), 221-223 (with N.M. Stephens).
  2. Spaces of matrices with several zero eigenvalues, Bull. London Math. Soc. 12 (1980), 89-95.
  3. Large spaces of matrices of bounded rank, Quart. J. Math. 31 (1980), 253-262 (with S. Lloyd).
  4. Primitive spaces of matrices of bounded rank, J. Austral. Math. Soc. 30 (1981), 473-482 (with S. Lloyd).
  5. Spaces of linear transformations of equal rank, Linear and Multilinear Algebra 13 (1983), 231-239 (with R. Westwick).
  6. Primitive spaces of matrices of bounded rank II, J. Austral. Math. Soc. 34 (1983), 306-315.
  7. A problem of Westwick on k-spaces, Linear and Multilinear Algebra 14 (1984), 263-273.
  8. Extensions to the Kronecker-Weierstrass theory of pencils, Linear and Multilinear Algebra 29 (1991), 235-241.