摘要
n阶实对称正定矩阵在矩阵理论中,对它的不等式研究具有有十分重要的意义.为此,文献[1-3]对著名的Minkowski不等式进行了不同程度的推广.在此基础上,将给定的n阶正定矩阵A,构造出一个n+m阶正定矩阵.利用该矩阵,将文献[1]中的不等式推广到正有理数n/m的情形.然后应用极限将正有理数的情形推广到正实数.从而推广了文献[1]中的结论,并应用推广的结果重新证明了古典的Hǒlder不等式与Minkowski不等式.
In the matrix theory, n-order real symmetric positive definite matrix is important to the study of inequality. For this reason, the well-known Minkowski inequality was generalized in reference [1-3]. Based on these generalizations, an n-f-m-order positive definiete matrix was constructed from a given n-order positive difinite matrix A. With the new matrix, first the inequality in reference [1] was extended to the case of positive rational number n/m, then by taking the limit, the above case was further extended to the case of positive real number. At last the classic Hǒlder inequality and Minkowski inequality were proved by the extended results in this paper.
出处
《浙江工业大学学报》
CAS
2006年第3期351-354,共4页
Journal of Zhejiang University of Technology
