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1. All numbers considered below are real. We shall write (i) (yu ■ ■ • ,yn) < (xi, ■ • • ,x ") to indicate that yi + • ■■+% ^ xi +■■■+ xk ik = 1, • • • , n — 1), yi + • • • + yn = xi + • • • + x " ; here Si, ■ ■ ■ , x " denote the numbers X\, • ■ • , x " arranged in non-ascending order of magnitude, and similarly for the y's. All matrices we consider are of(More)
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