A factorization theorem for matrices
A factorization theorem for matrices
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矩阵因式分解定理
DOI：
10.1080/03081088608817711
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
A. Sourour
中科院分区：
文献类型：
--
作者：
A. Sourour
证明了一个非标可逆方阵可以写成两个具有给定特征值的方阵的乘积，只要满足明显的行列式条件。作为推论，我们给出了一些已知结果的简短证明，如Ballantine的产品的四个或五个正定矩阵的特征，交换子定理的Shoda-汤普森领域有足够多的元素和其他结果。
It is shown that a nonscalar invertible square matrix can be written as a product of two square matrices with prescribed eigenvalues subject only to the obvious determinant condition. As corollaries, we give short proofs of some known results such as Ballantine's characterization of products of four or five positive definite matrices, the commutator theorem of Shoda-Thompson for fields with sufficiently many elements and other results.