# Why Table is not giving me the same sequence for eigenvalues of matrix

Let consider a matrix and evaluate the time dependent eigenvalues

M[t_]:={{Sin[t],Cos[t]},{t,t*t}};
e1[t_]:= Eigenvalues[M[t]]


Now If I evaluate

N@e1[1]


it gives output {1.66005, 0.181422}

But if I evaluate a table for different t

 N@Table[Evaluate[e1[i]], {i, 1, 5}] // FullSimplify


it gives first eigen value {0.181422, 1.66005} and all in form {{0.181422, 1.66005}, {1.20732, 3.70197}, {0.490124, 8.651}, {-0.599291, 15.8425}, {-1.01345, 25.0545}}

• Eigenvalues are sorted from largest to smallest when computed numerically. This sorting doesn't happen when working with exact numbers of symbolic expressions. This is mentioned in the documentation. Feb 18 '15 at 20:05
• Evaluate causes the Eigenvalues to be found symbolically before substituting the numeric i. Try this: Evaluate[e1[i]] /. i -> 1 // N Feb 18 '15 at 20:08
• george2079@ It also gives me the same result as table. can I evaluate for other eigenvalues? Evaluate[e1[i]] /. i -> {1,2,3,4,5} // N Feb 18 '15 at 21:50

Please check your definitions. You use e1 and eg.

Here is what I think you're asking:

M[t_] := {{Sin[t], Cos[t]}, {t, t*t}};
e1[t_] := Eigenvalues[M[t]];

e1[0]


(* {0, 0} *)

... a degenerate matrix.

N@Table[e1[i], {i, 1, 5}] // FullSimplify


(* {

{1.66005, 0.181422},

{3.70197, 1.20732},

{8.651, 0.490124},

{15.8425, -0.599291},

{25.0545, -1.01345}

} *)

...a list of the two eigenvalues for five different values of $i$.

If you want to include the "degenerate" example, just change the iterator to {i, 0, 5}.