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From Thomas Neidhart <>
Subject Re: [math] documentation for what pseudo-inverse means in decomp solvers
Date Sat, 19 Oct 2013 08:23:36 GMT
On 10/19/2013 01:21 AM, Phil Steitz wrote:
> The decomposition solvers can "invert" non-square matrices.  There
> is no documentation describing what exactly is being returned in
> these cases.  It is not obvious to me exactly what conditions the
> returned value satisfies in each case when the actual parameter is
> not square.  Do all of them return pseudo-inverses X satisfying AXA
> = A where A is the input matrix?  Do they satisfy other conditions
> as well?  Under what conditions will exceptions be thrown?  We
> should either throw NonSquareMatrixException (as MatrixUtils now
> does) on non-square arguments or define precisely what is being
> computed by each of the solvers for non-square arguments and what
> the preconditions are.

LU and Cholesky decomposition already check if the matrix is square and
throw a NonSquareMatrixException in this case.

QR decomposition seems to compute the right-inverse of the matrix if the
number of rows is equal to its rank.


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