I dug through some online Mathcad manual. genvecs is defined in terms of another function genvals.
Given M,N real-valued square matrices of the same size, genvals(M,N) returns a vector v of eigenvalues, each of which satisfies the generalized eigenvalue equation M x = v_j N x for nonzero eigenvectors x.
genvecs(M,N) returns the matrix of eigenvectors corresponding to genvals(M,N), so the jth column of genvecs(M,N) is the eigenvector x satisfying M x = v_j N x, where j = genvals(M, N).
As far as I can tell, the equivalent Maple command is simply the two-argument form of LinearAlgebra:-Eigenvectors
, with the output=vectors option. The equivalent of genvals is the two-argument form of LinearAlgebra:-Eigenvalues
, or LinearAlgebra:-Eigenvectors
with the output=values option.
Here is an example (stolen from the help page ?LinearAlgebra,Eigenvectors):
> M := Matrix([[6.,8.,5.],[8.,8.,9.],[5.,9.,6.]], datatype = float):
> N := Matrix([[6.,3.,3.],[3.,8.,8.],[3.,8.,9.]], datatype = float):
> LinearAlgebra:-Eigenvectors(M, N, output=vectors);
[0.102604389547461192 + 0. I 0.657926936009840757 + 0. I -0.722787575511656067 + 0. I]
[-0.735167353706277727 + 0. I 0.699410581470925828 + 0. I 0.0525410432222221321 + 0. I]
[0.670075593713203022 + 0. I -0.279207781766920516 + 0. I 0.689070068616467024 + 0. I ]
> LinearAlgebra:-Eigenvalues(M, N);
[-4.55651173111531005 + 0. I]
[1.56423606281299010 + 0. I ]
[0.223044899071558001 + 0. I]
You can get both results simultaneously by calling LinearAlgebra:-Eigenvectors with the option output=[values, vectors] (which is also the default).