EXERCISE 8.1
Prove that

is the covariance of the centered
data matrix, where

is the matrix formed
by the columns

.
EXERCISE 8.2
Compute the SVD of the French food data (Table
B.6).
EXERCISE 8.3
Compute

for the French food data
(Table
B.6).
EXERCISE 8.4
Apply the factorial techniques to the Swiss bank notes (Table
B.2).
EXERCISE 8.5
Apply the factorial techniques to the time budget data (Table
B.14).
EXERCISE 8.6
Assume that you wish to analyze

independent identically distributed
random variables. What is the percentage of the inertia
explained by the first factor? What is the percentage of the inertia
explained by the first

factors?
EXERCISE 8.7
Assume that you have

i.i.d. r.v.'s. What does the eigenvector,
corresponding to the first factor, look like.
EXERCISE 8.8
Assume that you have two random variables,

and

.
What do the eigenvalues and eigenvectors of their correlation
matrix look like? How many eigenvalues are nonzero?
EXERCISE 8.9
What percentage of inertia is explained by the first factor
in the previous exercise?
EXERCISE 8.10
How do the eigenvalues and eigenvectors in Example
8.1
change if we take the prices
in $ instead of in EUR? Does it make a difference if
some of the prices are in EUR and others in $?