Linear Operators Preserving t-Congruence on Matrices zyxwvutsrqponmlkjih Yoo-Pyo Hong Department of Mathematical Sciences Northern Illinois University De Kalb, lllinois 60115 Roger A. Horn Department of Mathematical Sciences The Johns Hopkins University Baltimore, Maryland 21218 and Chi-Kwong Li* Department of Mathematics The College of William and May Williamsburg, Virginia 23185 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK Submitted by Richard A. Brualdi ABSTRACT zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Two complex or real square matrices A and B are said to be t-congruent if there exists a nonsingular matrix S such that A = zyxwvutsrqponmlkjihgfedcbaZYXWV SBS’. If A and B are complex (respectively, real) and S IS unitary (respectively, real orthogonal), we say that they are unitarily t-congruent (respectively, real orthogonally congruent). In this note we obtain characterizations of linear operators on various matrix spaces that preserve t-congruence. Results and problems concerning unitary t-congruence or orthogonal t-congruence are discussed. *Research supported by NSF grant DMS 8940922. This research was finished while the author was visiting the Department of M athematical Sciences, The Johns Hopkins University, Baltimore, M aryland 21218, in the spring semester, 1991. LINEAR ALGEBRA AND ITS APPLICATIONS 175: lQl-211(1992) 0 Elsevier Science Publishing Co., Inc., 1992 191 655 Avenue of the Americas, New York, NY 10010 0024-3795/92/$5.00