Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-alge...Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-algebra aulomorphism, of Tn＋1 （R）. Furthermore we prove that this aulomorphism is an involutive Jordan automorphism of Tn＋1 （R）.展开更多
In this paper, two kinds of generalized Pascal matrices Pn,k and Qn,k, and two kinds of generalized Pascal functional matrices On,k[x,y] and Qn,k[x,y] are introduced and studied. Factorization of Pascal matrices into ...In this paper, two kinds of generalized Pascal matrices Pn,k and Qn,k, and two kinds of generalized Pascal functional matrices On,k[x,y] and Qn,k[x,y] are introduced and studied. Factorization of Pascal matrices into products of (0,1) Jordan matrices is established. Factorization of Pascal functional matrices into products of bidiagonal matrices is obtained.展开更多
We give an affirmative answer to the open problem proposed by Dr， Fuzhen Zhang in the paper 'Quaternions and matrices of quaternious'( LA A251:21-57 ) ,that is, there exists a 2n × 2n complex matrix B ...We give an affirmative answer to the open problem proposed by Dr， Fuzhen Zhang in the paper 'Quaternions and matrices of quaternious'( LA A251:21-57 ) ,that is, there exists a 2n × 2n complex matrix B such that, for any n×n complex matrices A1, A2展开更多
文摘Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-algebra aulomorphism, of Tn＋1 （R）. Furthermore we prove that this aulomorphism is an involutive Jordan automorphism of Tn＋1 （R）.
基金Development Program for Outstanding Young Teachers in Lanzhou University of Technology(Q02018)
文摘In this paper, two kinds of generalized Pascal matrices Pn,k and Qn,k, and two kinds of generalized Pascal functional matrices On,k[x,y] and Qn,k[x,y] are introduced and studied. Factorization of Pascal matrices into products of (0,1) Jordan matrices is established. Factorization of Pascal functional matrices into products of bidiagonal matrices is obtained.
文摘We give an affirmative answer to the open problem proposed by Dr， Fuzhen Zhang in the paper 'Quaternions and matrices of quaternious'( LA A251:21-57 ) ,that is, there exists a 2n × 2n complex matrix B such that, for any n×n complex matrices A1, A2
