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I use Mathematica version 9.0.1.

matA = DiagonalMatrix[ConstantArray[1, 3]];

matB = Normal[SparseArray[{Band[{1, 1}] -> 200, Band[{1, 2}] -> -100, 
 Band[{2, 1}] -> -100}, {3, 3}]];

{matA, matB} gives

{{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{200, -100, 0}, {-100, 200, -100}, {0, -100, 200}}}

e1 = Eigenvalues[{matB, matA}] gives an error:

Eigenvalues::exnum: Eigenvalues has received a matrix with non-numerical or exact elements. >>

e2 = Eigenvalues[N@{matB, matA}] gives the answer:

{341.421, 200., 58.5786}

Question: Why would e1 give an error when both matrices are numerical? I don't understand why N@{matB, matA} is needed to get their eigenvalues.

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    $\begingroup$ The phrase is "non-numerical or exact". Since the elements do not have decimal places, Mathematica is loathe to introduce imprecision which is required by the algorithm, hence the message. So, by using N you tell it you deliberately add the imprecision, making the decision for it. $\endgroup$ – rcollyer Feb 9 '14 at 20:45
  • $\begingroup$ @rcollyer You should probably make that an answer. It is the answer. $\endgroup$ – Szabolcs Feb 9 '14 at 20:50
  • $\begingroup$ @user11946 Can you please choose a display name? The generic "user11946" is hard to remember ... $\endgroup$ – Szabolcs Feb 9 '14 at 20:51
  • $\begingroup$ @rcollyer - It is subtle but I can see it now. Thanks for the insight. $\endgroup$ – user11946 Feb 9 '14 at 21:12
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    $\begingroup$ @user11946. No one is asking you to display your real name. Just change your username to something memorable. $\endgroup$ – RunnyKine Feb 9 '14 at 22:01
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This is rcollyer's comment posted as an answer because as Szabolcs says, it is the answer.

The phrase is "non-numerical or exact". Since the elements do not have decimal places, Mathematica is loathe to introduce imprecision which is required by the algorithm, hence the message. So, by using N you tell it to deliberately add the imprecision, making the decision for it.

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