Relation to Permutation Matrices

Recall that an x permutation matrix is a matrix having entries 1 and all the rest zero, such that no two of the ones are in a common row, or common column. To relate 6e-matrices with permutation matrices, the main burden will be carried by a theorem of D. Konig  

Theorem 5. (Konig) v) Suppose.4 is anmatrix of non-negative real numbers such that each row sum and each column sum is a fixed number =0- Then there exists in. 4 a family of n non-zero entries, with no two of them being in the same row or column. 

To apply this theorem, we require the notion of a correction for each 6s-matrix. 

We also observe that B has at least one diagonal entry zero in fact, if 

Remark 1. Although B is a symmetric matrix, it is NOT true that the can be chosen to be symmetric matrices. 

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