When working on an exercise for my students in order to reduce a symmetric matrix with an orthogonal transition matrix, I fell on the following error :
> with(LinearAlgebra): > A:=Matrix(3,3,[[2,-2,-2],[2,-2],[2]],scan=triangular,shape=symmetric); > T:=Eigenvectors(A); > T2:=T[2]; > B:=[Column(T2,1..3)]; > U:=GramSchmidt(B,'normalized'); Error, (in LinearAlgebra:-LA_Main:-Normalize) datatype of in-place Vector (algebraic) and datatype of result (anything) do not agree
It is the option ’normalized’ which causes the trouble.
I think that the problem comes from the "datatype" of the elements of the resulting matrix T2 as we can see below but it is impossible to modify this option.
> VectorOptions(B[1]); shape = [], datatype = algebraic, orientation = column, storage = rectangular, order = Fortran_order > MatrixOptions(T2); shape = [], datatype = algebraic, storage = rectangular, order = Fortran_order