Inequalities for sums of matrix quadratic forms Original Research Article

An attainable upper matrix bound is derived for image, improving upon earlier bounds by Anderson and Taylor [Linear Algebra Appl. 30:93–99 (1980)] and Olkin [Linear Algebra Appl. 52/53:529–532 (1983)]. Inequalities for the sum of harmonic means or parallel sums are derived as special cases. The more general problem of obtaining an upper bound for image is also considered.