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Author(s): |
Shiqiang Zhang, Dept. of Mathematics, Chongqing Medical University, Chongqing, China, 400016;Lab. of Forensic Medicine and Biomedicine Information, Chongqing Medical University, Chongqing, China, 400016
Chunli Wang, Dept. of Mathematics, Chongqing Medical University, Chongqing, China, 400016;Lab. of Forensic Medicine and Biomedicine Information, Chongqing Medical University, Chongqing, China, 400016 |
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Abstract: |
In management science and engineering research, a large number of cases analysis often require from qualitative analysis to quantitative analysis, linear algebra is often used in quantitative analysis. In linear algebra, the elementary transformation of matrix in rows and the elementary transformation of matrix in columns are fundamental operation. Literature [1] found that it is not mutually independent between the three elementary transformation of matrix. At the same time, literature [1] pointed out that method in literature [2] to solve relative largest linearly independent group with the elementary transformation is wrong. The cause of the error is that they don’t know that the elementary transformations are not independent among each other. The geometric significance of elementary transformations is discussed in this article, the cause of the error is not mutual independency among the elementary transformations. The real reason for the error occurred is that there is no clear geometric meaning of elementary transformation. The best way is given to solve relative largest linearly independent group of vectors by the elementary transformation. Some examples of the method are demonstrated.
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