TOEPLITZ DETERMINANTS AND POSITIVE SEMIDEFINITENESS

被引：1
|
作者：
MAKHOUL, J
机构：
[1] Bolt Beranek and Newman Inc., Cambridge
来源：
IEEE TRANSACTIONS ON SIGNAL PROCESSING | 1991年 / 39卷 / 03期
关键词：
Determinants - Positive Semidefinite Matrices - Toeplitz Matrices;
D O I：
10.1109/78.80862
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
We explore the role that the determinants of real, symmetric, Toeplitz matrices play in testing for their positive semidefiniteness. We show that the "leading principal minor" test used to test for positive definiteness is not sufficient in general to test for positive semidefiniteness of Toeplitz matrices, except in certain cases. We derive several properties and show in which cases the leading principal minor test is indeed sufficient. We then present a simple method for testing the positive semidefiniteness of all symmetric Toeplitz matrices.
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页码：743 / 746
页数：4
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