sqrm {FRAPO}

Square root of a quadratic matrix

Description

This function returns the square root of a quadratic and diagonalisable matrix.

Usage

sqrm(x, ...)

Arguments

x

matrix, must be quadratic.

...

The ellipsis argument is passed down to eigen().

Details

The computation of the square root of a matrix is based upon its eigen values and corresponding eigen vectors. The square matrix A is diagonisable if there is a matrix V such that D = V^{-1}AV, whereby D is a diagonal matrix. This is only achieved if the eigen vectors of the (n \times n) matrix A constitute a basis of dimension n. The square root of A is then A^{1/2} = V D^{1/2} V'.

Value

A matrix object and a scalar in case a (1 \times 1) matrix has been provided.

Author(s)

Bernhard Pfaff

See Also

eigen

Examples

data(StockIndex)
S <- cov(StockIndex)
SR <- sqrm(S)
all.equal(crossprod(SR), S)