Comparison theorems for symmetric functions of characteristic roots

Marvin Marcus
1961 Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics  
Several theorems are proved t hat g ive necessar y and suffi cien t cond it ions for A -B to be pos itive semidefi~li te Hermitian . The cond i t i~ll s a re in te rms of t he comparison of elementar y sy mmetl"l c functIOn s of t he charactel"lstlc roots of A + X a nd B + X as X va ri es over posit ive definite H ermi t ia n matrices.
doi:10.6028/jres.065b.010 fatcat:mhyuhjjtpjh4piz4fuk5arsz3q