| 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 |
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 13:01 | 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
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