General Matrix Power

Description

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

Usage

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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

See Also

Packages corpcor and expm define similar functions.

Examples

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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)