SOME INEQUALITIES FOR DETERMINANTS OF LEADING SUBMATRICES

A.A. Maleev
VANT. Ser.: Mat. Mod. Fiz. Rroc 1990. Вып.2. С. 54-57.

      Some properties of matrices and leading submatrices are studied, expressions describing the relation between elements of a matrix, determinants of leading submatrices, and algebraic complements are derived. These relations contain new nontrivial estimates for the determinants of leading submatrices. For matrices with an irreducibly dominant diagonal, the nondegeneracy of their leading submatrices is proved.