Eigenstuff in Mathematica

Lines in boldface are the inputs you type.  Hitting the Enter key (or Shift-Return) will result in Mathematica generating the given ouput.

Enter the matrix as a list of lists.  Lists begin and end with curly bracekts.  List items are separated by commas.

a = {{1, -1, 4}, {3, 2, -1}, {2, 1, -1}}

Use the MatrixForm function to view the matrix as an array.

MatrixForm[a]

Here is an alternate syntax:

a // MatrixForm

The Eigenvalues function takes a matrix as input and returns the eigenvalues.

Eigenvalues[a]

The Eigenvectors function takes a matrix as input and returns eigenvectors as a list of lists.  Each inner list gives the components of an eigenvector.

Eigenvectors[a]

The Eigensystem function takes a matrix as input and returns eigenvalues and corresponding eigenvectors in a list of lists.  The first list gives the eigenvalues and the remaining lists give eigenvectors in an order corresponding to the order in which the eigenvalues are given.

Eigensystem[a]