Introduction. We shall call a square matrix A of order n an Hadamard matrix or for brevity an iî-matrix, if each element of A has the value ± 1 and if the determinant of A has the maximum possible value w. It is known that such a matrix A is an iï-matrix [ l] if, and only if, AA'~nEn where A f is the transpose of A and En is the unit matrix of order n. It is also known that, if an iï-matrix of ...

On the Hopf structure of U p,q (gl(1|1)) and the universal T-matrix of F un p,q (GL(1|1)) Abstract Using the technique developed by Fronsdal and Galindo (Lett. Math. Phys. 27 (1993) 57) for studying the Hopf duality between the quantum algebras F un p,q (GL(2)) and U p,q (gl(2)), the Hopf structure of U p,q (gl(1|1)), dual to F un p,q (GL(1|1)), is derived and the corresponding universal T-matr...

Abstract Let $\mathcal{B}_{\mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type with braiding matrix $\mathfrak{q}$, $\mathcal{L}_{\mathfrak{q}}$ the corresponding Lusztig as in [ 4], and $\operatorname{Fr}_{\mathfrak{q}}: \mathcal{L}_{\mathfrak{q}} \to U(\mathfrak{n}^{\mathfrak{q}})$ quantum Frobenius map 5]. We prove that Lie $\mathfrak{n}^{\mathfrak{q}}$ is either 0 or pos...

(including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory. In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations and their optimal approximation problem over generalized reflexive matrix solution (X1,X2, . . . ,Xq). When the general coupled matrix equations are consistent o...