保持矩阵张量积幂等性的线性映射的进一步结果

Further results on linear maps preserving idempotence of tensor products of matrices

研究特征不是2域上的全矩阵空间的保矩阵张量积的幂等性的线性映射,给出了这类映射的具体形式。利用矩阵空间保幂等线性映射的结果,恰当运用矩阵的各种相似变换,应用幂等矩阵的性质和分块矩阵的运算技巧,得到了一个没有阶数限制的这类映射的刻画。结果表明这类映射都是规范的,这是对现有结论的一个推广。

Consider linear maps preserving idempotence of tensor products of matrices over a field of characteristic not 2.The concrete form of the maps under consideration is given.Based on the results of linear maps preserving idempotence on matrix space,a characterization of such maps without any restriction on order number is obtained by appropriately applying some similar transformations of matrices,the properties of idempotent matrices and the operation techniques of blocked matrices.The results show that all such maps have normal form,which is a generalization of the existing conclusions.