# Square root of a symmetric, positive semi-definite matrix

### Description

Calculation of the square root of a positive semi-definite matrix (see Details for the definition of such a matrix).

### Usage

1 | ```
sqrtmatrix(mat)
``` |

### Arguments

`mat` |
numeric matrix. |

### Details

The matrix `mat`

must be symmetric and positive semi-definite. Otherwise, there is an error.

The square root of the matrix `mat`

is the positive semi-definite matrix `M`

such as `t(M) %*% M = mat`

.
Do not confuse with `sqrt(mat)`

, which returns the square root of the elements of `mat`

.

The computation is based on the diagonalisation of `mat`

. The eigenvalues smaller than 10^-16 are identified as null values.

### Value

Matrix: the square root of the matrix `mat`

.

### Author(s)

Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Sabine Demotes-Mainard.

### Examples

1 2 3 | ```
M2 = matrix(c(5, 4, 4, 5), nrow = 2)
M = sqrtmatrix(M2)
M
``` |

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