{{page>wiki:headers:hheader}}



===== Lecture: Finding Eigenvalues and Eigenvectors (?? minutes) =====

Give a mini-lecture on how to calculate eigenvalues and eigenvectors.  It is often easiest to do this with an example.  We like to use the matrix  
$$A_7\doteq\pmatrix{1&2\cr 9&4\cr}$$
from the [[courses:activities:pract:prlineartrans|Linear Transformations]] activity since the students have already seen this matrix and know what it's eigenvectors are.

  - We like to start by asking the students what they remember from their math classes about eigenvalues and eigenvectors.  Typically our students remember that "It has something to do with a determinant and a $\lambda$,"  but not much else.
  - Introduce the eigenvalue equation.  If you have used the Linear Transformations activity, then students should know geometrically that the eigenvectors of a transformation are the vectors that are only changed by a scale.  If you get the students to say this in words, you can write the eigenvalue equation $A\vert v\rangle =\lambda \vert v\rangle$ on the board immediately afterwards.  This will help them see how the algebraic statement is connected to the geometric statement.
  - Demonstrate methods to solve the characteristic equation using your chosen example.
  - Demonstrate methods to find the eigenvectors associated with a given eigenvalue using your chosen example.

{{page>wiki:footers:courses:spfooter}}