论文信息 - Strong forms of nonsingularity

Strong forms of nonsingularity

Abstract Motivated by certain views of the sign nonsingular matrices, we begin study of several classes of nonsingular matrices naturally intermediate between sign nonsingular matrices and the ordinary nonsingular matrices. These all involve Hadamard products that allow constrained changes in the magnitudes (but not the signs) of entries, or the selection of patterns of subblocks. Among a wide variety of results is the fact that the nonsingular matrices A for which A·A -1 T is doubly stochastic arise as one of our “strong” forms of nonsingularity.

Charles R. Johnson | P. van den Driessche | John H. Drew

[1] John Maybee,et al. Qualitative Economics and the Scope of the Correspondence Principle , 1968 .

[2] P. M. Gibson,et al. Conversion of the permanent into the determinant , 1971 .

[3] Interpolation of D-stability and sign stability , 1988 .

[4] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5] G. Lady,et al. Qualitatively invertible matrices , 1983 .

[6] Charles R. Johnson,et al. Mathematical aspects of the relative gain array ( AΦHA —T ) , 1986 .

[7] Carsten Thomassen. When the sign pattern of a square matrix determines uniquely the sign pattern of its inverse , 1989 .

[8] Charles R. Johnson. Hadamard products of matrices , 1974 .

[9] Charles R. Johnson. Combinatorial matrix analysis: An overview , 1988 .

[11] C. Thomassen. Sign-Nonsingular Matrices and Even Cycles in Directed Graphs , 1986 .