Hi
I have the following matrix


A=[a\_11 a\_12 a\_13 1;
 a\_21 a\_22 a\_23 1;
 .
 .
 .
 a\_n1 a\_n2 a\_n3 1]


I have seen that when some of a\_ij are big for instance in the order of 200 , then condition
number is also big.


I would like to know is it possible to show it theoretically. 


Is it possible to find a lower bound for this problem?


Regards,


Reza



condition number
One possible way to proceed would be to get the singular value decomposition of your matrix and then look at the ratio of the largest singular value to the smallest singular value (a.k.a. the 2-norm condition number); largeness of this condition number implies largeness of the condition number with respect to the other norms of interest, and you can probably just manipulate inequalities at that point.


