Vol. 51, No. 2, 1974

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The Hadamard product of A and A

Charles Royal Johnson

Vol. 51 (1974), No. 2, 477–481

Coefficient-wise multiplication was introduced by Hadamard and has been studied for certain square matrices by I. Schur and later authors. For A Mn(C), the n by n complex matrices, this paper examines the Hadamard product of A and A. Upper estimates are given for the largest characteristic root of this necessarily Hermitian product, and three conditions on A sufficient for the product to be positive definite are presented.

Mathematical Subject Classification 2000
Primary: 15A42
Received: 26 January 1973
Published: 1 April 1974
Charles Royal Johnson