R: Matrix Condition

cond {pracma} | R Documentation

## 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))

[Package pracma version 2.0.4 Index]