Condition number of empty matrix
조회 수: 3(최근 30일)
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 2022년 6월 23일
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.