Matrix Inequalities and Twisted Inner Products
Thomas H. Pate · Birkhäuser Basel eBooks · 2010
We will demonstrate that several known inequalities involving generalized Schur functions, also known as generalized matrix functions, follow from either the Cauchy-Schwartz inequality, or from certain monotonicity relations that exist between inner products on spaces of multilinear functions. Connections between our inner products and permanent inequalities are presented, and a connection to some unresolved problems in partial differential equations is indicated.