August 2014 Archives

Ascending The Eigen

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

  M × vi = λi × vi

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

  |M - λi × 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.

Full text...  

At The Foot Of The Eigen

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.

Full text...