R: Matrix Power

matpow {DescTools} | R Documentation

## Matrix Power

### Description

Compute the k-th power of a matrix. Whereas `x^k` computes element wise powers, `x %^% k` corresponds to k - 1 matrix multiplications, `x %*% x %*% ... %*% x`.

### Usage

    x %^% k

### Arguments

`x` | a square `matrix`.
`k` | an integer, k >= 0.

### Details

Argument k is coerced to integer using `as.integer`.

The algorithm uses O(log2(k)) matrix multiplications.

### Value

A matrix of the same dimension as `x`.

### Note

If you think you need `x^k` for k < 0, then consider instead `solve(x %^% (-k))`.

### Author(s)

Based on an R-help posting of Vicente Canto Casasola, and Vincent Goulet's C implementation in actuar.

### See Also

`%*%` for matrix multiplication.

### Examples

    A <- cbind(1, 2 * diag(3)[,-1])
    A
    A %^% 2
    stopifnot(identical(A, A %^% 1),
              A %^% 2 == A %*% A)

[Package DescTools version 0.99.24 Index]