Invertibility of combinations of two quadratic matrices
Tao Xie · Journal of Baoji University of Arts and Sciences · 2010
Aim To study the relationship between the invertibility of the combination aP+bQ-cPQ and the coefficients a,b,c,where P,Q are two matrices satisfying the equation(x-α)(x-β)=0(which is called quadratic matrices).Methods By investigating the relationship between the kernel space of aP+bQ-cPQ and coefficients a,b,c,the relationship between the invertibility of the combination aP+bQ-cPQ and the coefficients a,b,c,is discussed.Results The invertibility of aP+bQ-cPQ are independent of the choice of the coefficients a,b,c with ab≠0,when α,β takes some values.Conclusion The results extend the conclusions of the existing literature,and enrich the related theory of linear combinations of special matrices.