Image Processing Reference
In-Depth Information
3.15 Consider the following square matrix:
2
4
3
5
220
002
002
A ¼
(a) Compute A 7 and A 73 using the Cayley
Hamilton theorem.
-
(b) Compute e At using the Cayley
Hamilton theorem.
-
3.16 Assume that the following matrix is nonsingular:
2
4
3
5
a 10
0 b 0
00c
C ¼
Compute the natural logarithm of the matrix C; that is, identify the matrix
B ¼ ln ( C )
es the equation C ¼ e B . Is the assumption of non-singu-
larity of C really needed for the solution of this problem?
that satis
3.17 Given the 3
3 matrix
2
4
3
5
324
10
A ¼
1
215
Express the matrix polynomial f ( A ) ¼ A 4
2A 3
þ A 2
þ
A þ
3I as a linear
combination of the matrices A 2 , A, and I only.
3.18 Let the 2
2 matrix A be de
ned as
07
A ¼
10
Compute A k and e At .
3.19
Let the 3
3 matrix A be de
ned as
2
4
3
5
0
30
A ¼
30
3
0
30
Compute A k and e At .
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