# Exponentiation of a matrix (including pseudoinverse)

March 22, 2012
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(This article was first published on me nugget, and kindly contributed to R-bloggers)

The following function "exp.mat" allows for the exponentiation of a matrix (i.e. calculation of a matrix to a given power). The function follows three steps:
1) Singular Value Decomposition (SVD) of the matrix
2) Exponentiation of the singular values
3) Re-calculation of the matrix with the new singular values

The most common case where the method is applied is in the calculation of a "Moore–Penrose pseudoinverse", or a matrix raised to the power of -1. In this case, the function returns the same result as the "pseudoinverse" function from the corpcor package (although maybe not as nicely implemented). This should also be analogous to the pinv function in Matlab.

Less common is the need to calculate other powers of matrices. For example, I use this function to calculate the square root of a matrix (and square root of the inverse of a matrix) within Canonical Correlation Analysis (CCA). I hope to write a post shortly on the use of CCA in identifying coupled patterns in climate data.

Below is the code for the exp.mat function as well as some demonstrations of its use in R.

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