Condition number of empty matrix
3 ビュー (過去 30 日間)
Robert van de Geijn 2022 年 6 月 20 日
if is a 0 x 0 matrix, then cond( A ) returns 0. However, we know that the condition number is always >= 1. Also, one could argue that the empty matrix is an identity matrix, and hence its condition number should equal 1.
Any particular reason why matlab made this choice?
Christine Tobler 2022 年 6 月 23 日
The case of a 0-by-0 matrix doesn't have any very useful definition, as you note correctly in the comments above.
MATLAB does what it does because it computes any p-condition number using the formula:
norm(A, p) * norm(inv(A), p)
and of course the norm of  is 0, as is the norm of the inverse of .
A legitimate question could be if the norm of a  matrix should be 0, or if it should be NaN since this matrix can't be mulitplied with a vector that has norm 1. But in practical terms, I think it's more useful to define this norm as being 0 than returning NaN.