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Condition number with respect to inversion


c = cond(X)
c = cond(X,p)


The condition number of a matrix measures the sensitivity of the solution of a system of linear equations to errors in the data. It gives an indication of the accuracy of the results from matrix inversion and the linear equation solution. Values of cond(X) and cond(X,p) near 1 indicate a well-conditioned matrix.

c = cond(X) returns the 2-norm condition number, the ratio of the largest singular value of X to the smallest.

c = cond(X,p) returns the matrix condition number in p-norm:

norm(X,p) * norm(inv(X),p)

If p is...

Then cond(X,p) returns the...


1-norm condition number


2-norm condition number


Frobenius norm condition number


Infinity norm condition number

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The algorithm for cond (when p = 2) uses the singular value decomposition, svd. When the input matrix is sparse, cond ignores any specified p value and calls condest.

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