sqrm {FRAPO} | R Documentation |
This function returns the square root of a quadratic and diagonalisable matrix.
sqrm(x, ...)
x |
|
... |
The ellipsis argument is passed down to |
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'
.
A matrix
object and a scalar in case a (1 \times 1)
matrix has been
provided.
Bernhard Pfaff
data(StockIndex)
S <- cov(StockIndex)
SR <- sqrm(S)
all.equal(crossprod(SR), S)