PHYCS 3730/6720 Lab Exercise
Reading and references:
Here we practice solving eigenvalue problems using Maple and
Python/numpy. The answer file
Use Python in interactive mode and use the numpy.linalg package
to find the eigenvalues and eigenvectors of the matrix
9 3 3
3 2 4
3 4 2
Copy your Python session (with the results) to the answer file.
To check your understanding, use Python (interactive mode) to verify
that the eigenvector for the eigenvalue 12 satifies the eigenvalue
equation: matrix times eigenvector equals eigenvalue times
eigenvector. Copy the new parts of your Python session to the answer
Use Maple to find the eigenvalues and eigenvectors of the same matrix.
Remember to use with(linalg). The functions eigenvals
and eigenvectors are what you are looking for. Be sure you
understand the output from the eigenvectors function. Copy
your Maple session to your answer file.
You may have noticed that the Maple and numpy eigenvectors are not the
same. This happens because the conventions for normalization are
different. Numpy normalizes the vectors to unit norm. Maple uses a
different normalization. To see that is is only a matter of
normalization, for each of the three eigenvectors, find the constant
that, when it multiplies the Maple eigenvector, the resulting product
matches the Python eigenvector. Do this by copying the Maple
eigenvectors to Python (one-by-one) and using Python to figure out the
normalization constant. In your answer file, for each eigenvector,
show the Maple eigenvector, the constant, the result of multiplying by
the constant, and the Python eigenvector for the sake of comparison.
Copy the relevant parts of your Python session to the answer file.