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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

1130.0. "A problem in matrix algebra" by HPSTEK::XIA (In my beginning is my end.) Mon Sep 25 1989 00:14

    Let A and B be n by n matrices with rank r and s respectively.  
    Let C = A*B.  Show that the rank of C is always greater or equal to 
    r+s-n.
    
    Eugene

T.R	Title	User	Personal Name	Date	Lines
1130.1	yawn...	ALLVAX::ROTH	If you plant ice you'll harvest wind	`Mon Sep 25 1989 15:01`	5
	The worst that can happen is that the range of B overlaps the kernel of A maximally; if s < dim ker (A) = n-r then rank AB = 0, else rank AB = s - dim ker (A) = s-(n-r) = r+s-n. - Jim