I have tried the following to get the eigenvalues of several matrices of the type:
J := D[{i - l*r - ux*r*x - uy*r*y, -mx*x + ex*ux*r*x, -my*y +
ey*uy*r*y}, {{r, x, y}}] // StandardForm
Then with three possible solutions given by Solve
FullSimplify[J/. Solve[i - l*r - ux*r*x - uy*r*y == 0 && -mx*x + ex*ux*r*x ==
0 && -my*y + ey*uy*r*y == 0, {r, x, y}]]
Eigenvalues[%[[1]]]
But it does not give me the eigenvalues, it just outputs:
Eigenvalues[{{-l, -((i ux)/l), -((i uy)/l)}, {0, -mx + (ex i ux)/l, 0}, {0, 0, -my + (ey i uy)/l}}]
Only the following code gives them:
FullSimplify[J/. Solve[i - l*r - ux*r*x - uy*r*y == 0 && -mx*x + ex*ux*r*x ==
0 && -my*y + ey*uy*r*y == 0, {r, x, y}]]
%[[1]]
Eigenvalues[%]
Why? In other words, why is
Function[%[[1]]]
different from
%[[1]]
Function[%]
?