mpower: General Matrix Power In mvinfluence: Influence Measures and Diagnostic Plots for Multivariate Linear Models

Description

Calculates the `n`-th power of a square matrix, where `n` can be a positive or negative integer or a fractional power.

Usage

 `1` ```mpower(A, n) ```

Arguments

 `A` A square matrix. Must also be symmetric for non-integer powers. `n` matrix power

Details

If `n<0`, the method is applied to A^{-1}. When `n` is an integer, the function uses the Russian peasant method, or repeated squaring for efficiency. Otherwise, it uses the spectral decomposition of `A`, requiring a symmetric matrix.

Value

Returns the matrix A^n

Author(s)

Michael Friendly

Packages corpcor and expm define similar functions.

Examples

 ```1 2 3 4 5 6 7 8 9``` ```M <- matrix(sample(1:9), 3,3) mpower(M,2) mpower(M,4) # make a symmetric matrix MM <- crossprod(M) mpower(MM, -1) Mhalf <- mpower(MM, 1/2) all.equal(MM, Mhalf %*% Mhalf) ```

mvinfluence documentation built on May 31, 2017, 1:59 a.m.