Karol Pak

Learn More
In formal proof checking environments such as Mizar it is not merely the validity of mathematical formulas that is evaluated in the process of adoption to the body of accepted formalizations, but also the readability of the proofs that witness validity. As in case of computer programs, such proof scripts may sometimes be more and sometimes be less readable.(More)
In this paper I present basic properties of block diagonal matrices over a set. In my approach the finite sequence of matrices in a block diagonal matrix is not restricted to square matrices. Moreover, the off-diagonal blocks need not be zero matrices, but also with another arbitrary fixed value. [10] provide the terminology and notation for this paper.
The paper is concerned with a generalization of concepts introduced in [13], i.e. introduced are matrices of linear transformations over a finite-dimensional vector space. Introduced are linear transformations over a finite-dimensional vector space depending on a given matrix of the transformation. Finally, I prove that the rank of linear transformations(More)