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
.
Search WWH ::
Custom Search