A BEST UPPER BOUND FOR THE 2-NORM CONDITION NUMBER OF A MATRIX

Let A be an n x n nonsingular real or complex matrix. The best possibl e upper bound for the ratio of the largest and smallest singular value s of A, using tr AA, det A, and n only, is obtained. A comparison wit h an earlier bound is given, and the singular and nonsquare cases are included. If all the eigenvalues of A are real and positive, the best possible upper bound for the ratio of the largest and smallest eigenva lues of A, involving tr A, det A, and n only, is presented as well. (C ) Elsevier Science Inc., 1997.