How can I access a variable using Position?

Question

I want to define a vector PosVec[a, b] dependent on the variables a and b of a matrix VecMat[a, b]. I want to calculate the "positions" in VecMat[a, b] of the maximum values in VecMatQ[a, b] and store them in PosVec[a, b] .

My problem is that, with my code below, I can't access the variables a and b of PosVec by PosVec[a, b] -> PosVec[1, 1] For the positions in VecMatQ where there are entries of a and b, Position generates empty spaces as shown below:

Here is my code:

Remove["Global`*"]

m = {{1, -a + b, 3}, {b, -6, 4}, {3, b, 0}};

VecMat[a_, b_] = Eigenvectors[m];

VecMatQ[a_, b_] = VecMat[a, b]*Conjugate[VecMat[a, b]];

PosVec[a_, b_] = 
  Table[Position[VecMatQ[a, b][[i]], Max[VecMat[a, b][[i]]]], {i, 1, 3}] // Flatten;

PosVec[1, 1]

{{},{},{}}

but

Table[Position[VecMatQ[1, 1][[i]], Max[VecMat[1, 1][[i]]]], {i, 1, 3}] // Flatten

gives the right values

{(3),(2),(1)}

Can someone help me to make the evaluation of Position dependent on the variables a and b?

Answer 1

Shortest way: change PosVec[a_, b_] = to PosVec[a_, b_] :=, i.e. use SetDelayed instead of Set. Longest (but cleaner I think) way: change all Set to SetDelayed, define m as a two-args function, and modify the right-hand side of your second definition accordingly. – Xavier 19 hours ago

Yes that works thx!