K. Manjunatha Prasad
Abstract
In this paper, we consider an m x n regular matrix A over a commutative ring A (-a matrix whose range is direct summand of A m ) and a necessary and sufficient condition in terms of determinantal rank is obtained for solvability of Ax = b. In the light of this result we define rank-function for matrices.
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In this paper, we consider an m x n regular matrix A over a commutative ring A (-a matrix whose range is direct summand of A m ) and a necessary and sufficient condition in terms of determinantal rank is obtained for solvability of Ax = b. In the light of this result we define rank-function for matrices.
Key concepts: Mathematics, Rank (graph theory), Commutative ring, Matrix (chemical analysis), Pure mathematics, Ring (chemistry), Function (biology), Commutative property