The Inverse of a Boolean Matrix
Robert S. Ledley · 1965
Abstract : The paper describes the necessary and sufficient conditions for a Boolean matrix to have a left and a right inverse. Boolean matrices are arrays of Boolean functions just as ordinary matrices are arrays of numbers. The rules for Boolean matrix multiplication are the same as for ordinary matrix multiplication, except that summation is replaced by logical summation, and the product is replaced by a logical product. Note that the elements of the matrices might just be 0 or 1, which would be treated as a 'universally true' and a 'universally false' Boolean function, i.e. the least upper bound and the greatest lower bound of all the Boolean functions. Use is made of the partition of the Boolean matrices.