linear algebra - Problem with Eigenvectors when given a matrix containing approximate numbers and symbols

I'm trying to diagonalize a certain 2 x 2 matrix, but Mathematica refuses to find the eigenvectors. In particular, when I input

Eigenvectors[{{1.8741*10^7 + 1.40161*10^6 B, 2.79374*10^7}, 
              {2.79374*10^7, -3.1235*10^7 - 1.40161*10^6 B}}]

(B is a parameter). I receive the error

Eigenvectors::eivec0: Unable to find all eigenvectors

and the bogus output

{{0, 0}, {0, 0}}

On the other hand, Mathematica has no problem with the eigenvalues, for some reason. Can someone help me figure out what's going on here?

Answer

Although the documentation could be clearer on this point, Eigenvectors doesn't like to work symbolically on a matrix containing elements with approximate numbers. The solution is to Rationalize the matrix.

data = {{1.8741*10^7 + 1.40161*10^6 B, 2.79374*10^7}, 
        {2.79374*10^7, -3.1235*10^7 - 1.40161*10^6 B}};
Eigenvectors[Rationalize[data]] // Column

eigenvectors

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