PROOFS PROGRAMME

150 Matrix Sets to Diagonalize

For page specific messages
For page specific messages


This sample contains 150 sets of $3\times 3$ matrices for computing eigenvectors and eigenvalues.

Why so many sets?

The primary reason for creating so many sets was to give each students a different assignment and to give them extra sets for practise purposes. A large number $3\times3$ of matrices were generated starting with the Jordan canonical form with diagonal entries varied over a range of values. Then a similarity transform was applied by number of  different sets of  invertible matrices on each one of the matrices in Jordan form. Finally, those problems were discarded where the matrices, or the eigenvalues, or the eigenvectors had some large elements. Mathematica was used to write the \LaTeX code of the matrices, their eigenvalues
and eigenvectors. One \LaTeX file was generated for each matrix and stored. These were then input in a main \LaTeX file which  generated the final PDF file of all sets with all answers at the end.