AbstractTwo square matrices A and B over a ring R are semisimilar, written A⋍B, if YAX=B and XBY=A for some (possibly rectangular) matrices X, Y over R. We show that if A and B have the same dimension, and if the ring is a division ring D, then A⋍B if and only if A2 is similar to B2 and rank(Ak)=rank(Bk), k=1,2,
AbstractIn this paper, as a generalization of prime Boolean matrices and prime fuzzy matrices, we st...
AbstractLet A be an n-by-n matrix with real entries. We show that a necessary and sufficient conditi...
Suppose that A and B are two complex n×n matrices. What is the sufficient or necessary condition suc...
AbstractTwo square matrices A and B over a ring are pseudosimilar if there exist X, Y, and Z satisfy...
Two matrices over an arbitrary semiring are R-related if their column spaces are equal and are L-rel...
AbstractIt is well known that if A and B are n × m matrices over a ring R, then coker A ≅ coker B do...
AbstractThe paper studies the problem on matrix similarity over a commutative rings. The conditions ...
Let A be an n-by-n matrix with real entries. We show that a necessary and sufficient condition for A...
AbstractLet D be a division ring with an involution J such that D is finite-dimensional over its cen...
This paper treats linear algebra over a semiring pair, in a wide range of applications to tropical a...
In this paper answers are provided to the following questions: Given a matrix E1 of order k × m, doe...
AbstractRoth's theorem on the solvability of matrix equations of the form AX−YB=C is proved for matr...
AbstractIt is shown that Roth's theorems on the equivalence and similarity of block diagonal matrice...
Let R be an associative ring. We define a subset SR of R as SR = [a ? R | aRa = (0)] and call it the...
Throughout this paper D will denote a division ring with involution *, and S = (xCDIx*=x) and K = (x...
AbstractIn this paper, as a generalization of prime Boolean matrices and prime fuzzy matrices, we st...
AbstractLet A be an n-by-n matrix with real entries. We show that a necessary and sufficient conditi...
Suppose that A and B are two complex n×n matrices. What is the sufficient or necessary condition suc...
AbstractTwo square matrices A and B over a ring are pseudosimilar if there exist X, Y, and Z satisfy...
Two matrices over an arbitrary semiring are R-related if their column spaces are equal and are L-rel...
AbstractIt is well known that if A and B are n × m matrices over a ring R, then coker A ≅ coker B do...
AbstractThe paper studies the problem on matrix similarity over a commutative rings. The conditions ...
Let A be an n-by-n matrix with real entries. We show that a necessary and sufficient condition for A...
AbstractLet D be a division ring with an involution J such that D is finite-dimensional over its cen...
This paper treats linear algebra over a semiring pair, in a wide range of applications to tropical a...
In this paper answers are provided to the following questions: Given a matrix E1 of order k × m, doe...
AbstractRoth's theorem on the solvability of matrix equations of the form AX−YB=C is proved for matr...
AbstractIt is shown that Roth's theorems on the equivalence and similarity of block diagonal matrice...
Let R be an associative ring. We define a subset SR of R as SR = [a ? R | aRa = (0)] and call it the...
Throughout this paper D will denote a division ring with involution *, and S = (xCDIx*=x) and K = (x...
AbstractIn this paper, as a generalization of prime Boolean matrices and prime fuzzy matrices, we st...
AbstractLet A be an n-by-n matrix with real entries. We show that a necessary and sufficient conditi...
Suppose that A and B are two complex n×n matrices. What is the sufficient or necessary condition suc...
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