matrix condition number
1 Matrix Condition Number
if is non-singular; and if is singular.
The condition number is a measure of stability or sensitivity of a matrix (or the linear system it represents) to numerical operations. In other words, we may not be able to trust the results of computations on an ill-conditioned matrix.
Matrices with condition numbers near 1 are said to be well-conditioned. Matrices with condition numbers much greater than one (such as around for a Hilbert matrix) are said to be ill-conditioned.
If is the condition number of , then measures a sort of inverse distance from to the set of singular matrices, normalized by . Precisely, if is invertible, and , then must also be invertible. On the other hand, in the case of the -norm, there always exists a singular matrix such that (so the distance estimate is sharp).
- 1 Golub and Van Loan. Matrix Computations, 3rd edition. Johns Hopkins University Press, 1996.
|Title||matrix condition number|
|Date of creation||2013-03-22 13:04:17|
|Last modified on||2013-03-22 13:04:17|
|Last modified by||stevecheng (10074)|
|Synonym||matrix condition number|