2 added 26 characters in body edited Jul 22 '15 at 3:08 tparker 97055 silver badges2121 bronze badges [This is what Wolfram tech support told me when I filed a bug report:] That is because using machine precision (inexact) numbers such 0. (as opposed to exact numbers like 0) forces Eigenvectors[] to seach for eigenvectors numerically and hence the error message. For example, please evaluate and compare the results of the following expression used with machine precision and exact numbers: Eigenvectors[{{Cos[1. x], Exp[I x]}, {1, 0}}] Eigenvectors[{{Cos[1 x], Exp[I x]}, {1, 0}}]  [This is what Wolfram tech support told me:] That is because using machine precision (inexact) numbers such 0. (as opposed to exact numbers like 0) forces Eigenvectors[] to seach for eigenvectors numerically and hence the error message. For example, please evaluate and compare the results of the following expression used with machine precision and exact numbers: Eigenvectors[{{Cos[1. x], Exp[I x]}, {1, 0}}] Eigenvectors[{{Cos[1 x], Exp[I x]}, {1, 0}}]  [This is what Wolfram tech support told me when I filed a bug report:] That is because using machine precision (inexact) numbers such 0. (as opposed to exact numbers like 0) forces Eigenvectors[] to seach for eigenvectors numerically and hence the error message. For example, please evaluate and compare the results of the following expression used with machine precision and exact numbers: Eigenvectors[{{Cos[1. x], Exp[I x]}, {1, 0}}] Eigenvectors[{{Cos[1 x], Exp[I x]}, {1, 0}}]  1 answered Jul 22 '15 at 1:42 tparker 97055 silver badges2121 bronze badges [This is what Wolfram tech support told me:] That is because using machine precision (inexact) numbers such 0. (as opposed to exact numbers like 0) forces Eigenvectors[] to seach for eigenvectors numerically and hence the error message. For example, please evaluate and compare the results of the following expression used with machine precision and exact numbers: Eigenvectors[{{Cos[1. x], Exp[I x]}, {1, 0}}] Eigenvectors[{{Cos[1 x], Exp[I x]}, {1, 0}}]