Value-at-Risk Theory and Practice
The first advanced book on value-at-risk
Chapter 2, Page 73 Exercise 7
Find the eigenvalues and eigenvectors of the matrix
[2.74]
Solution
Denote the matrix c. We first find its eigenvalues. These are values such that
for some non-zero vector v. This is possible only if the determinant of is zero, a condition that yields the equation
2 – 5 + 4 = 0
[s1]
Solutions are = 1 and = 4. Substituting these into [2.68] and solving, we obtain corresponding eigenvectors
and
[s2]
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such that
is zero, a condition that yields the equation
and
