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文[1]讨论了二阶方阵的平方根和三角方阵的三角平方根问题,但其结论有误.这里指出其错误并给出正确的定理.定义1设A是一个n阶方阵,若存在n阶方阵B,使B2=A,则称方阵B为方阵A的平方根.若有Bm=A,则称B为A的m次方根.文[1]给出如下定理:上(下)三角方阵存在上(下)三角?
The paper [1] discussed the square root of the second-order square matrix and the triangular square root of the triangular square matrix, but its conclusion was wrong. Here pointed out its error and gives the correct theorem. Definition 1 Let A be an n-order square matrix. If there is an n-order square matrix B and let B2 = A, square matrix B is the square root of square matrix A. If Bm=A, then B is said to be the mth root of A. The following theorem is given in [1]: The upper (lower) triangular square exists in the upper (lower) triangle?