ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


determinant

On Determinant Zeros of Boolean Matrices

The properties of exteriority and interiority of square matrices with elements from arbitrary Boolean algebra are studied in this paper. The exteriorandinte riorparts formade generatepart of a matrix with zerodeterminant. Itisshown, inparticular, that the setof exteriorparts is a normal setinthe Boolean algebraofall Booleans quarematrices and it is a lower semilattice. The set of interior parts is an upper semilattice. Moreover linear combinations and even polynomials of the interiorities also belong to it.

Cramer’s Formulas for Systems of Linear Equations and Inequalities Over Boolean Algebra

There obtained analogies of classical Cramer’s formulas for systems of linear equations and inequalities with square matrix of coefficients from Boolean algebra.