EXERCISE 2.1
Compute the determinant for a

matrix.
EXERCISE 2.2
Suppose that

. Is it possible that all eigenvalues
of

are positive?
EXERCISE 2.3
Suppose that all eigenvalues of some (square) matrix

are different from zero. Does the
inverse

of

exist?
EXERCISE 2.4
Write a program that calculates the Jordan decomposition of the matrix
Check Theorem
2.1 numerically.
EXERCISE 2.6
Show that a projection matrix only has eigenvalues in

.
EXERCISE 2.7
Draw some iso-distance ellipsoids for the metric

of Example
3.13.
EXERCISE 2.8
Find a formula for

and for

(Hint: use the inverse partitioned matrix with

)
EXERCISE 2.9
Prove the Binomial inverse theorem for
two non-singular matrices

and

:

(Hint: use (
2.26) with

)