Square-zero factorization of matrices

For given m x n matrices G and F over an arbitrary field F, necessary and sufficient conditions (in terms of rank, amongst others) are presented for F to divide G with a square-zero quotient. These results are then used to extend the results of Novak [3] on square-zero factorization to matrices over an arbitrary field. The ranks that the square-zero factors can have are also investigated. Formulae are also presented by which these quotients can be constructed when this type of division is possible. (C) 2015 Elsevier Inc. All rights reserved.