Assignment 4

Multivariate Data Analysis
Psychology 6140

Readings

Interactive Rank Exercise: Here you get to try out your understanding of the rank of a matrix online! Try several exercises at difficulty level 1, then try several at level 2. Highly recommended.
Linear Transformations Applet: Enter coefficients for a 2 × 2 matrix, and see the effect it has as a linear transformation.
Linear transformations of points Another online linear transformation applet.
imlproj.sas: Projections: Projecting a vector in a vector space, and the Gram-Schmidt process, in excruciating detail!

From the Matrix Algebra Problems (MAP) handout:

Try using my SAS IML matrix library or R to do the following problems from Green and Carroll. For SAS, start your session with

ods listing;
proc iml;
   %include iml(matlib);
   reset print log;

which defines functions proj(y,X) (project y on X), R(X) (rank of matrix X) among others.

For R, there is a similar collection of functions in the matlib package you can load into your R session.

library(matlib)

Chap 3, Problem 7 -- part (a) only. For this problem, try to follow G&C's approach or that in the IML example imlproj. You can create a matrix X containing all three vectors (as columns) with the expression
```
X = t({ 1 2 3,  3 0 2, 3 1 1});
```
You can use the gsorth function to verify your results.
Chap 4, Problem 7. For this problem, you can use the R(X) function to verify your answer, but use some other method to find the rank.
Chap 4, Problem 9b