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I want to calculate the conditioning of a matrix, therefore I use the cond() commando in Matlab. A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned.

If I calculate the condition number of the matrix:

-0.0053 -0.0031

0.0031 -0.0053

the condition number is equal to 1. This means that the matrix is well-conditioned. However if I calculate the determinant of this matrix with the command det() the result is 3.7700e-005. Thus almost zero what means that the matrix is almost singular, thus ill-conditioned. Why is the condition number 1 while the matrix is ill-conditioned?

Steven

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# Condition number of a matrix is 1 but determinant is almost 0

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