The rank of block matrix over division ring
Jingfang Shen · Journal of Natural Science of Heilongjiang University · 2004
Matrix category with a zero object over division ring is an Abel category. In this category, solving the homo- # A geneous linear equation set ( A, B )X = 0(or X = 0) have close contact with seeking the pushout for morphisms B # A {A,B}(or the pullback for morphisms {A,B}) .The homogeneous linear equation sets ( A, B )X = 0 and X = 0 are B discussed and the relationship between block matrixes are studied over division ring. Some formulas of rank about block matrixes and the submatrixes over division ring are given.