Matrix Square Root
This function computes the matrix square root of a square matrix. The sqrt of a matrix A is S such that A = S S.
sqrtm(x)
x |
a square matrix. |
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.
A matrix ‘as x’ with the matrix sqrt of x.
Michael Stadelmann wrote the first version.
Higham, N.~J. (2008). Functions of Matrices: Theory and Computation; Society for Industrial and Applied Mathematics, Philadelphia, PA, USA.
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))
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