On 10/19/2013 01:21 AM, Phil Steitz wrote:
> The decomposition solvers can "invert" nonsquare 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 pseudoinverses 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 nonsquare arguments or define precisely what is being
> computed by each of the solvers for nonsquare 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 rightinverse of the matrix if the
number of rows is equal to its rank.
Thomas

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