Vol. 44, No. 1, 1973

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The Jacobian of a growth transformation

Donald Steven Passman

Vol. 44 (1973), No. 1, 281–290

The transformation T, described in a paper of Baum and Eagon, is frequently a growth transformation which affords an iterative technique for maximizing certain functions. In this paper, the Jacobian matrix J of T is studied. It is shown, for example, that the eigenvalues of J are real and nonnegative in a large number of cases. In addition, these eigenvalues are considered at critical points of T. One necessary assumption used throughout is that the function P to be maximized is homogeneous in the variables involved.

Mathematical Subject Classification 2000
Primary: 26A57
Secondary: 60J99
Received: 31 August 1971
Published: 1 January 1973
Donald Steven Passman