August 2014 Archives

In the previous post we covered eigensystems of two by two matrices, being the set of unit eigenvectors v_i and eigenvalues λ_i that satisfy the relation

  M × v_i = λ_i × v_i

To find the eigenvalues of a matrix M we solved the characteristic equation

  |M - λ_i × I| = 0

Now for a two by two matrix this was a simple quadratic equation that we could solve with the equation we learnt in school. For larger matrices the characteristic equation is much harder to solve and we shall have to take an entirely different approach.

Over the last couple of posts we've covered the arithmetic of vectors and matrices and now we're ready to explore some more advanced aspects of linear algebra, starting with eigensystems.