# sqrm: Square root of a quadratic matrix In FRAPO: Financial Risk Modelling and Portfolio Optimisation with R

## Description

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

## Usage

 1 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

eigen
 1 2 3 4 data(StockIndex) S <- cov(StockIndex) SR <- sqrm(S) all.equal(crossprod(SR), S)