Vol. 15, No. 3, 1965

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A subdeterminant inequality

Marvin David Marcus and H. Minc

Vol. 15 (1965), No. 3, 921–924
Abstract

Let A be an n-square positive semi-definite hermitian matrix and let Dm(A) denote the maximum of all order m principal subdeterminants of A. In this note we prove the inequality

(Dm (A ))1∕m ≧ (Dm+1 (A ))1∕(m+1),  m = 1,⋅⋅⋅ ,n− 1,

and discuss in detail the case of equality. This result is closely related to Newton’s and Szász’s inequalities.

Mathematical Subject Classification
Primary: 15.58
Secondary: 15.20
Milestones
Received: 27 August 1964
Published: 1 September 1965
Authors
Marvin David Marcus
H. Minc