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

sqrtmatrix(mat)

Arguments

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

    M2 = matrix(c(5, 4, 4, 5), nrow = 2)
    M = sqrtmatrix(M2)
    M

Results