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Matrix Condition NumberThe condition number for matrix inversion with respect to a matrix norm k¢k of a square matrix A is defined by∙(A)=kAkkA¡1k;
if A is non-singular; and ∙(A)=+1 if A 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 105 for a 5£5Hilbert matrix) are said to be ill-conditioned.
If ∙(A) is the condition number of A , then ∙(A) measures a sort of inverse distance from A to the set of singular matrices, normalized by kAk . Precisely, if A isinvertible, and kB¡Ak
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