Reading
Lay, 4.9 Applications to Markov Chains (282-290)
Lay, 5.1 Eigenvectors and Eigenvalues (295-302)
Lay, 5.2 The Characteristic Equation (305-311)
Homework
Please find the eigenvalues and eigenvectors of
$$A \rightarrow \left[ {\begin{array}{cc}
1 & 0 \\
0 & -1 \\
\end{array} } \right]$$
|
$$B \rightarrow \left[ {\begin{array}{cc}
0 & -1 \\
1 & 0 \\
\end{array} } \right]$$
|
Discussion
Q: It's nice that eigenvectors and eigenvalues help me compute time-courses of simple deterministic systems by hand, but I can use a computer. Why do I care?
A: Linear algebra, vector spaces, eigenvectors, and eigenvalues are the mother tongue of quantum mechanics. If you are familiar with eigenvectors and eigenvalues, it's much easier to explain how the postulates of quantum mechanics have as one of their consequences the Heisenberg uncertainty relationship. If you don't know about eigenvalues and eigenvectors, quantum indeterminism seems not merely spooky or philosophically weird--it also becomes an ill-defined buzzword.
