Psychology 6140

- Green & Carroll,
- Tabachnick & Fidell (Regression), 5.1-5.4
- Stevens, (eigenvalues) 2.6; (regression) 3.1-3.9

- R: See the matlib vignettes,
`"eigen-ex1"`and`"eigen-ex2"` - These demonstrate some properties of eigenvalues and eigenvectors.
- EigenExplorer
- Some Java applets that allow you to visually explore the properties of eigenvectors and eigenvalues of 2x2 and 3x3 matrices. Go to Eigenvalues and Eigenvectors.

- Use the
`eigen()`function to find the eigenvalues and eigenvectors of the following matrices:+- -+ +- -+ A = | 5 4 | | 2 2 -4 | | 4 8 | B = | 2 4 2 | +- -+ | -4 2 2 | +- -+

e.g.,`r <- eigen(A)`. - Verify that for each matrix above, (a) the trace of the matrix is the sum of the latent roots, and (b) the determinant is the product.
- Without direct calculation, find the latent roots of (a) A
^{ -1}; (b) B^{2}.

* © 1995 Michael Friendly*