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Problem
Problem
If
A
=
[
1
2
0
1
]
A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}
A
=
[
1
0
2
1
]
,
P
=
[
cos
θ
sin
θ
−
sin
θ
cos
θ
]
P = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}
P
=
[
cos
θ
−
sin
θ
sin
θ
cos
θ
]
,
Q
=
P
T
A
P
Q = P^T A P
Q
=
P
T
A
P
, find
P
Q
2014
P
T
PQ^{2014} P^T
P
Q
2014
P
T
: (a)
[
1
2
2014
0
1
]
\begin{bmatrix} 1 & 2^{2014} \\ 0 & 1 \end{bmatrix}
[
1
0
2
2014
1
]
(b)
[
1
4028
0
1
]
\begin{bmatrix} 1 & 4028 \\ 0 & 1 \end{bmatrix}
[
1
0
4028
1
]
(c)
(
P
T
)
2013
A
2014
P
2013
(P^T)^{2013} A^{2014} P^{2013}
(
P
T
)
2013
A
2014
P
2013
(d)
P
T
A
2014
P
P^T A^{2014} P
P
T
A
2014
P
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