pinv | R Documentation |
Compute the pseudoinverse of a matrix using the SVD-construction
pinv(A, eps = 1e-08)
A |
[numeric] matrix |
eps |
[numeric] tolerance for determining zero singular values |
The Moore-Penrose pseudoinverse (sometimes called the generalized inverse) \boldsymbol{A}^+ of a matrix \boldsymbol{A} has the property that \boldsymbol{A}^+\boldsymbol{AA}^+ = \boldsymbol{A}. It can be constructed as follows.
Compute the singular value decomposition \boldsymbol{A} = \boldsymbol{UDV}^T
Replace diagonal elements in \boldsymbol{D} of which the absolute values are larger than some limit eps
with their reciprocal values
Compute \boldsymbol{A}^+ = \boldsymbol{UDV}^T
S Lipshutz and M Lipson (2009) Linear Algebra. In: Schuam's outlines. McGraw-Hill
A <- matrix(c( 1, 1, -1, 2, 2, 2, -1, 3, -1, -1, 2, -3 ),byrow=TRUE,nrow=3) # multiply by 55 to retrieve whole numbers pinv(A) * 55
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