Assignment 7
1. Create simple matrices (preferably at most 3x4) and show that
1. Ax(B+C) = (AxB)+(AxC)
2. (A+B)T = AT + BT
3. (AxB) T = BT x AT
2. Show that the determinant of a diagonal matrix is the product of the diagonal elements
3. Find the “inverse” of your diagonal matrix (same diagonal matrix from question 2)
4. Generate the variance-covariance matrix (S) for the USArrets data using Centering and Indempotent matrices (see hint on the next slide) and compare your result with the built-in R function for calculating the variance-covariance matrix
5. Calculate the “trace” of this variance-covariance matrix. What does this result mean/show?
6. Calculate the “determinant” this variance-covariance matrix. What does this result mean/show?
7. Compare the results of “trace” and “determinant” calculations. Which one has a larger value? Why?
8. Find the eigen values and eigen vectors for the variance-covariance matrix of the USArrets data
• Comment on your findings. Such as, how many positive eigen values, how many zero eigen values, what does this tell you about the rank of the variance-covariance matrix ?
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