I agree. It makes no sense at all to me for A.abs() to return the determinant of A.
For real or complex matrices it would make sense for A.abs() to be sqrt(trace(A^*A)) where A^* is the conjugate transpose. This is just the square root of the sums of the squares of the absolute values of the entries, i.e. the standard Hermitian norm. John On Apr 4, 5:35 pm, "Justin C. Walker" <[email protected]> wrote: > On Apr 4, 2011, at 15:19 , John H Palmieri wrote: > > > > > > > > > > > On Monday, April 4, 2011 3:00:20 PM UTC-7, pong wrote: > > >> By that I simply mean a function that on input a real matrix M returns > >> the matrix N such that n[i][j] = abs(m[i][j]). > > >> This can be achieve by something like: > > >> n = len(M.rows()); m =len(M.columns()); N = matrix(n,m,lambda i,j: > >> abs(M[i][j])); > > >> However, for a square matrix M, M.abs() returns something which wasn't > >> what one expected: > > >> B = matrix(2,2,lambda i,j: i-j); B; B.abs() > > >> returns > > >> [ 0 -1] > >> [ 1 0] > > >> and 1 > > >> Is it a bug? Or something that I missed? > > > For matrices, B.abs() returns the determinant. If you type "B.abs?", you'll > > see a message like > > > Return the absolute value of self. (This just calls the __abs__ > > method, so it is equivalent to the abs() built-in function.) > > > Then if you type "B.__abs__?", you'll see > > > Synonym for self.determinant(...). > > I suppose this is because the determinant is sometimes written as > |1 0| > |0 -1| > but I think that's carrying things too far. I'd say this violates the > Principle of Least Surprise... > > I see two "bugs": that introspection claims that ".abs()" is defined in the > file it claims: > ======================= > sage: B.abs? > String Form: <built-in method abs of > sage.matrix.matrix_integer_dense.Matrix_integer_dense object at 0x10ce3a4d0> > Namespace: Interactive > Definition: B.abs(self) > Docstring: > > Return the absolute value of self. (This just calls the __abs__ > method, so it is equivalent to the abs() built-in function.) > ======================= > > (which is not the case); and the use of "abs" (in any form) for determinant. > > But that's just me. > > Justin > > -- > Justin C. Walker > Curmudgeon-at-large > Director > Institute for the Absorption of Federal Funds > ---- > 186,000 Miles per Second > Not just a good idea: > it's the law! > ---- -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
