A Complement on the Singnlarity of a Bordered Matrix

Abstract:

      Let consider a m×n matrix A with rank q1 matrix with rank r₁ and H is a r₂×n matrix with rank r₂. Paper [4] gave the necessary and sufficient conditions for the nonsingularity of the bordered matrix M with the case in which r₁=M-q and r₂>n-q . In this short paper, we give the necessary and sufficient conditions for nonsingnlarity of M with the ease in which r₁≥m-q and r₂≥n-q.