mpower
From matlib v0.9.2
by Michael Friendly
Matrix Power
A simple function to demonstrate calculating the power of a square symmetric matrix in terms of its eigenvalues and eigenvectors.
Usage
mpower(A, p, tol = sqrt(.Machine$double.eps))
Arguments
- A
a square symmetric matrix
- p
matrix power, not necessarily a positive integer
- tol
tolerance for determining if the matrix is symmetric
Details
The matrix power p
can be a fraction or other non-integer. For example, p=1/2
and
p=1/3
give a square-root and cube-root of the matrix.
Negative powers are also allowed. For example, p=-1
gives the inverse and p=-1/2
gives the inverse square-root.
Value
A
raised to the power p
: A^p
See Also
The {%^%}
operator in the expm package is far more efficient
Examples
# NOT RUN {
C <- matrix(c(1,2,3,2,5,6,3,6,10), 3, 3) # nonsingular, symmetric
C
mpower(C, 2)
zapsmall(mpower(C, -1))
solve(C) # check
# }
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