sqrm {FRAPO}R Documentation

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 AA is diagonisable if there is a matrix VV such that D=V1AVD = V^{-1}AV, whereby DD is a diagonal matrix. This is only achieved if the eigen vectors of the (n×n)(n \times n) matrix AA constitute a basis of dimension nn. The square root of AA is then A1/2=VD1/2VA^{1/2} = V D^{1/2} V'.

Value

A matrix object and a scalar in case a (1×1)(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)

[Package FRAPO version 0.4-1 Index]