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 |
|
... |
The ellipsis argument is passed down to |
Details
The computation of the square root of a matrix is based upon its eigen
values and corresponding eigen vectors. The square matrix is
diagonisable if there is a matrix
such that
,
whereby
is a diagonal matrix. This is only achieved if the eigen
vectors of the
matrix
constitute a basis of
dimension
. The square root of
is then
.
Value
A matrix
object and a scalar in case a matrix has been
provided.
Author(s)
Bernhard Pfaff
See Also
Examples
data(StockIndex)
S <- cov(StockIndex)
SR <- sqrm(S)
all.equal(crossprod(SR), S)
[Package FRAPO version 0.4-1 Index]