cond {pracma}

Matrix Condition

Description

Condition number of a matrix.

Usage

cond(M, p = 2)

Arguments

M

Numeric matrix; vectors will be considered as column vectors.

p

Indicates the p-norm. At the moment, norms other than p=2 are not implemented.

Details

The condition number of a matrix measures the sensitivity of the solution of a system of linear equations to small errors in the data. Values of cond(M) and cond(M, p) near 1 are indications of a well-conditioned matrix.

Value

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

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

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

(Not yet implemented.)

Note

Not feasible for large or sparse matrices as svd(M) needs to be computed. The Matlab/Octave function condest for condition estimation has not been implemented.

References

Trefethen, L. N., and D. Bau III. (1997). Numerical Linear Algebra. SIAM, Philadelphia.

See Also

normest, svd

Examples

cond(hilb(8))