sqrtm {expm} | R Documentation |

## Matrix Square Root

### Description

This function computes the matrix square root of a square matrix.
The sqrt of a matrix `A`

is `S`

such that `A = S S`

.

### Usage

```
sqrtm(x)
```

### Arguments

`x` |
a square matrix. |

### Details

The matrix square root `S`

of `M`

, `S = sqrtm(M)`

is
defined as one (the “principal”) `S`

such that
`S S = S^2 = M`

, (in **R**, `all.equal( S %*% S , M )`

).

The method works from the Schur decomposition.

### Value

A matrix ‘as `x`

’ with the matrix sqrt of `x`

.

### Author(s)

Michael Stadelmann wrote the first version.

### References

Higham, N.~J. (2008).
*Functions of Matrices: Theory and Computation*;
Society for Industrial and Applied Mathematics, Philadelphia, PA, USA.

### See Also

### Examples

```
m <- diag(2)
sqrtm(m) == m # TRUE
(m <- rbind(cbind(1, diag(1:3)),2))
sm <- sqrtm(m)
sm
zapsmall(sm %*% sm) # Zap entries ~= 2e-16
stopifnot(all.equal(m, sm %*% sm))
```

[Package

*expm*version 0.999-9 Index]