[Gretl-users] Idempotency of residual maker matrix

gretl 2020e Windows 64 I created a "residual maker" matrix M = I - X*inv(X'X)*X', which is symmetric, non-invertible and  idempotent. Below I have copied its properties as printed out by gretl. It clearly states that the matrix is "Not idempotent". But It is, in theory and it is in practice: I performed the operation M*M - M, and I got a matrix with zeros or numbers raised to the 10^{-16} or even smaller. *What does it take for gretl to characterize a matrix as idempotent?* ************************************** Properties of matrix M Rows          50 Columns       50 Rank          47 Square Not idempotent 1-norm           3.0108809 Infinity-norm    3.0108809 Trace            47 Determinant      4.0749073e-047 Eigenvalues:   (1.586419e-015, 0)   (-1.300316e-015, 0)   (3.561026e-017, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 0)   (1, 5.5511151e-017)   (1, -5.5511151e-017)   (1, 0) -- Alecos Papadopoulos PhD Athens University of Economics and Business web: alecospapadopoulos.wordpress.com/ scholar:https://g.co/kgs/BqH2YU