On the class of square Petrie matrices induced by cyclic permutations.
On the diagonalisation of von Neumann regular matrices
On the diagonals of integral matrices
On the invertibility of a linear function on the quaternions.
On the matrix equation over finite fields.
On the maximal subgroup of the sandwich semigroup of generalized circulant Boolean matrices
Let be a positive integer, and the set of all -circulant matrices over the Boolean algebra , . For any fixed -circulant matrix () in , we define an operation “” in as follows: for any in , where is the usual product of Boolean matrices. Then is a semigroup. We denote this semigroup by and call it the sandwich semigroup of generalized circulant...
On the special trace decomposition problem on quaternion structure.
On unimodular complements
On various dynamic compensations
Orders in quaternion algebras.
Orders of some modular linear groups.
Perimeter preserver of matrices over semifields
For a rank- matrix , we define the perimeter of as the number of nonzero entries in both and . We characterize the linear operators which preserve the rank and perimeter of rank- matrices over semifields. That is, a linear operator preserves the rank and perimeter of rank- matrices over semifields if and only if it has the form , or with some invertible matrices U and V.
Permutation matrices and matrix equivalence over a finite field.
Polynomials and linear transformations over finite fields.
Power indices of trace zero symmetric Boolean matrices
The power index of a square Boolean matrix A is the least integer d such that Ad is a linear combination of previous nonnegative powers of A. We determine the maximum power indices for the class of n×n primitive symmetric Boolean matrices of trace zero, the class of n×n irreducible nonprimitive symmetric Boolean matrices, and the class of n×n reducible symmetric Boolean matrices of trace zero, and characterize the extreme matrices respectively.
Pseudo-similarity and partial unit regularity
Rank and perimeter preserver of rank-1 matrices over max algebra
For a rank-1 matrix over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T(A) = U ⊗ A ⊗ V, or with some monomial matrices U and V.
Remarques sur les matrices orthogonales (resp. symétriques) à coefficients -adiques
is not boundedly generated by elementary matrices: explicit proof.
Some inequalities for sums of nonnegative definite matrices in quaternions.