sqrm function

Square root of a quadratic matrix

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

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 c("$A^{1/2} = V\n$", "$D^{1/2} V'$").

Returns

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)