||Message]
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 practice purposes.
How were these sets generated?
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.
Matrix Diagonalisation; There are 150 different sets.
Each set has five 3x3 matrices to be
diagonlised. Out of five matrices there is one matrix of each of the following types.
(a) All three eigenvalues are distinct
(b) Two distinct eigenvalues, one eigenvalue has degeneracy 2; three linearly indepdendent
eigenvectors.
(c) Two disticnt eigenvalues and two linearly independent eigenvactors.
(d) Only one distinct eignevalue and two linearly indpendent eigenvectors.
(e) Only one distinct eigenvalue and only one linearly independent eigenvector.
Download: 150-MatrixSets.pdf (1014.7 KB)
