We show some upper bounds for the product of arbitrarily selected singular values of the sum of two matrices.The results are additional to our previous work on the lower bound eigenvalue inequalities of the sum of two...We show some upper bounds for the product of arbitrarily selected singular values of the sum of two matrices.The results are additional to our previous work on the lower bound eigenvalue inequalities of the sum of two positive semidefinite matrices.Besides,we state explicitly Hoffman’s minimax theorem with a proof,and as applications of our main results,we revisit and give estimates for related determinant inequalities of Hua type.展开更多
By presenting a counterexample, the author of paper （ZHAO Li-feng. J. Math. Res. Exposition, 2007, 27（4）： 949-954） declared that some assertions in papers of LU Yun-xia, ZHANG Shu-qing （J. Math. Res. Exposition,...By presenting a counterexample, the author of paper （ZHAO Li-feng. J. Math. Res. Exposition, 2007, 27（4）： 949-954） declared that some assertions in papers of LU Yun-xia, ZHANG Shu-qing （J. Math. Res. Exposition, 1999, 19（3）： 598-600）, HE Gan-tong （J. Math. Res. Exposition, 2002, 22（1）： 79-82） and YUAN Hui-ping （J. Math. Res. Exposition, 2001, 21（3）： 464-468） are wrong. In this note, we point out that the counterexample is wrong. Further discussion on these assertions and some related results are also given.展开更多
基金Xi’s work was partially supported by the National Natural Science Foundation of China(Grant No.11361038)。
文摘We show some upper bounds for the product of arbitrarily selected singular values of the sum of two matrices.The results are additional to our previous work on the lower bound eigenvalue inequalities of the sum of two positive semidefinite matrices.Besides,we state explicitly Hoffman’s minimax theorem with a proof,and as applications of our main results,we revisit and give estimates for related determinant inequalities of Hua type.
基金Supported by the Natural Science Foundation of Science and Technology Office of Guizhou Province (Grant No. J[2006]2002)
文摘By presenting a counterexample, the author of paper （ZHAO Li-feng. J. Math. Res. Exposition, 2007, 27（4）： 949-954） declared that some assertions in papers of LU Yun-xia, ZHANG Shu-qing （J. Math. Res. Exposition, 1999, 19（3）： 598-600）, HE Gan-tong （J. Math. Res. Exposition, 2002, 22（1）： 79-82） and YUAN Hui-ping （J. Math. Res. Exposition, 2001, 21（3）： 464-468） are wrong. In this note, we point out that the counterexample is wrong. Further discussion on these assertions and some related results are also given.
