how to prove the matrix A^(n) equals stuff [closed]
how to prove that A^(n) = U(n)A + V(n)I
the matrices I = (1 1 1)
(1 1 1)
(1 1 1)
the discription is in here please helpme out
I tried to find this in order to figuer out the equation of U(n) and V(n) you can see in here
matrices
asked Dec 7 at 15:02
plus plus
34
closed as off-topic by Michael Seifert, Xander Henderson, Leucippus, user10354138, Brahadeesh Dec 12 at 8:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Michael Seifert, Xander Henderson, Leucippus, user10354138, Brahadeesh
If this question can be reworded to fit the rules in the help center, please edit the question.
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how to prove that A^(n) = U(n)A + V(n)I
the matrices I = (1 1 1)
(1 1 1)
(1 1 1)
the discription is in here please helpme out
I tried to find this in order to figuer out the equation of U(n) and V(n) you can see in here
matrices
asked Dec 7 at 15:02
plus plus
34
closed as off-topic by Michael Seifert, Xander Henderson, Leucippus, user10354138, Brahadeesh Dec 12 at 8:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Michael Seifert, Xander Henderson, Leucippus, user10354138, Brahadeesh
If this question can be reworded to fit the rules in the help center, please edit the question.
Did you try to diagonalize $A$?
– Botond
Dec 7 at 15:07
sorry I didn't get it .. could U please give me more details
– plus plus
Dec 7 at 15:08
Can you calculate the eigenvectors and eigenvalues of $A$?
– Botond
Dec 7 at 15:11
actually not ... because we didnt talk about them in classes ..we are in a very low level yet .. but its a homework and we are not supposed to use stuff we didnt talk about it yet ... please have a look on the post again I added sth ..
– plus plus
Dec 7 at 15:15
Shouldn't $I$ be the identity matrix instead of the full $1$ matrix?
– Botond
Dec 7 at 15:25
|
show 2 more comments
how to prove that A^(n) = U(n)A + V(n)I
the matrices I = (1 1 1)
(1 1 1)
(1 1 1)
the discription is in here please helpme out
I tried to find this in order to figuer out the equation of U(n) and V(n) you can see in here
matrices
asked Dec 7 at 15:02
plus plus
34
how to prove that A^(n) = U(n)A + V(n)I
the matrices I = (1 1 1)
(1 1 1)
(1 1 1)
the discription is in here please helpme out
I tried to find this in order to figuer out the equation of U(n) and V(n) you can see in here
matrices
matrices
asked Dec 7 at 15:02
plus plus
34
asked Dec 7 at 15:02
plus plus
34
edited Dec 7 at 15:12
asked Dec 7 at 15:02
plus plus
34
asked Dec 7 at 15:02
plus plus
34
asked Dec 7 at 15:02
plus plus
34
34
closed as off-topic by Michael Seifert, Xander Henderson, Leucippus, user10354138, Brahadeesh Dec 12 at 8:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Michael Seifert, Xander Henderson, Leucippus, user10354138, Brahadeesh
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Michael Seifert, Xander Henderson, Leucippus, user10354138, Brahadeesh Dec 12 at 8:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Michael Seifert, Xander Henderson, Leucippus, user10354138, Brahadeesh
If this question can be reworded to fit the rules in the help center, please edit the question.
Did you try to diagonalize $A$?
– Botond
Dec 7 at 15:07
sorry I didn't get it .. could U please give me more details
– plus plus
Dec 7 at 15:08
Can you calculate the eigenvectors and eigenvalues of $A$?
– Botond
Dec 7 at 15:11
actually not ... because we didnt talk about them in classes ..we are in a very low level yet .. but its a homework and we are not supposed to use stuff we didnt talk about it yet ... please have a look on the post again I added sth ..
– plus plus
Dec 7 at 15:15
Shouldn't $I$ be the identity matrix instead of the full $1$ matrix?
– Botond
Dec 7 at 15:25
|
show 2 more comments
Did you try to diagonalize $A$?
– Botond
Dec 7 at 15:07
sorry I didn't get it .. could U please give me more details
– plus plus
Dec 7 at 15:08
Can you calculate the eigenvectors and eigenvalues of $A$?
– Botond
Dec 7 at 15:11
actually not ... because we didnt talk about them in classes ..we are in a very low level yet .. but its a homework and we are not supposed to use stuff we didnt talk about it yet ... please have a look on the post again I added sth ..
– plus plus
Dec 7 at 15:15
Shouldn't $I$ be the identity matrix instead of the full $1$ matrix?
– Botond
Dec 7 at 15:25
Did you try to diagonalize $A$?
– Botond
Dec 7 at 15:07
Did you try to diagonalize $A$?
– Botond
Dec 7 at 15:07
sorry I didn't get it .. could U please give me more details
– plus plus
Dec 7 at 15:08
sorry I didn't get it .. could U please give me more details
– plus plus
Dec 7 at 15:08
Can you calculate the eigenvectors and eigenvalues of $A$?
– Botond
Dec 7 at 15:11
Can you calculate the eigenvectors and eigenvalues of $A$?
– Botond
Dec 7 at 15:11
actually not ... because we didnt talk about them in classes ..we are in a very low level yet .. but its a homework and we are not supposed to use stuff we didnt talk about it yet ... please have a look on the post again I added sth ..
– plus plus
Dec 7 at 15:15
actually not ... because we didnt talk about them in classes ..we are in a very low level yet .. but its a homework and we are not supposed to use stuff we didnt talk about it yet ... please have a look on the post again I added sth ..
– plus plus
Dec 7 at 15:15
Shouldn't $I$ be the identity matrix instead of the full $1$ matrix?
– Botond
Dec 7 at 15:25
Shouldn't $I$ be the identity matrix instead of the full $1$ matrix?
– Botond
Dec 7 at 15:25
|
show 2 more comments
1 Answer
1
active
oldest
votes
Let's use induction:
For $n=2$, I will leave it to you to prove that
$$A^2=3A-2I$$
Now let's suppose that it's true for $n$:
$$A^n=u_nA+v_nI$$
And now we can use induction:
$$begin{align}
A^{n+1}&=A^nA\
&=(u_nA+v_nI)A\
&=u_nA^2+v_nA\
&=u_n(3A-2I)+v_nA\
&=(3u_n+v_n)A-2u_nI
end{align}$$
Can you continue the work?
answered Dec 7 at 15:31
Botond
5,4382732
Yuup thanks very very much
– plus plus
Dec 7 at 15:56
sorry for bothering again but how can I find the dimension of the vector field E, where , E=vect (A^(k)) , k belongs to Z
– plus plus
Dec 10 at 17:02
@plusplus Next time please make a new question. What so you mean by $text{vec}(A^k)$? Is it a vector space with basis $A^1,A^2,...$?
– Botond
Dec 10 at 17:10
Actually I thought it would be easier to continue in the same question .. I'm really sorry next time I'll do it .. yes it is a vector space with basis A^1,A^2,.. but also with( I , A^(-1) , A^(-2) .....)
– plus plus
Dec 10 at 17:13
@plusplus It's fine. First of all, can you find a basis if $k in mathbb{N}$ only?
– Botond
Dec 10 at 17:15
|
show 15 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Let's use induction:
For $n=2$, I will leave it to you to prove that
$$A^2=3A-2I$$
Now let's suppose that it's true for $n$:
$$A^n=u_nA+v_nI$$
And now we can use induction:
$$begin{align}
A^{n+1}&=A^nA\
&=(u_nA+v_nI)A\
&=u_nA^2+v_nA\
&=u_n(3A-2I)+v_nA\
&=(3u_n+v_n)A-2u_nI
end{align}$$
Can you continue the work?
answered Dec 7 at 15:31
Botond
5,4382732
Yuup thanks very very much
– plus plus
Dec 7 at 15:56
sorry for bothering again but how can I find the dimension of the vector field E, where , E=vect (A^(k)) , k belongs to Z
– plus plus
Dec 10 at 17:02
@plusplus Next time please make a new question. What so you mean by $text{vec}(A^k)$? Is it a vector space with basis $A^1,A^2,...$?
– Botond
Dec 10 at 17:10
Actually I thought it would be easier to continue in the same question .. I'm really sorry next time I'll do it .. yes it is a vector space with basis A^1,A^2,.. but also with( I , A^(-1) , A^(-2) .....)
– plus plus
Dec 10 at 17:13
@plusplus It's fine. First of all, can you find a basis if $k in mathbb{N}$ only?
– Botond
Dec 10 at 17:15
|
show 15 more comments
Let's use induction:
For $n=2$, I will leave it to you to prove that
$$A^2=3A-2I$$
Now let's suppose that it's true for $n$:
$$A^n=u_nA+v_nI$$
And now we can use induction:
$$begin{align}
A^{n+1}&=A^nA\
&=(u_nA+v_nI)A\
&=u_nA^2+v_nA\
&=u_n(3A-2I)+v_nA\
&=(3u_n+v_n)A-2u_nI
end{align}$$
Can you continue the work?
answered Dec 7 at 15:31
Botond
5,4382732
Yuup thanks very very much
– plus plus
Dec 7 at 15:56
sorry for bothering again but how can I find the dimension of the vector field E, where , E=vect (A^(k)) , k belongs to Z
– plus plus
Dec 10 at 17:02
@plusplus Next time please make a new question. What so you mean by $text{vec}(A^k)$? Is it a vector space with basis $A^1,A^2,...$?
– Botond
Dec 10 at 17:10
Actually I thought it would be easier to continue in the same question .. I'm really sorry next time I'll do it .. yes it is a vector space with basis A^1,A^2,.. but also with( I , A^(-1) , A^(-2) .....)
– plus plus
Dec 10 at 17:13
@plusplus It's fine. First of all, can you find a basis if $k in mathbb{N}$ only?
– Botond
Dec 10 at 17:15
|
show 15 more comments
Let's use induction:
For $n=2$, I will leave it to you to prove that
$$A^2=3A-2I$$
Now let's suppose that it's true for $n$:
$$A^n=u_nA+v_nI$$
And now we can use induction:
$$begin{align}
A^{n+1}&=A^nA\
&=(u_nA+v_nI)A\
&=u_nA^2+v_nA\
&=u_n(3A-2I)+v_nA\
&=(3u_n+v_n)A-2u_nI
end{align}$$
Can you continue the work?
answered Dec 7 at 15:31
Botond
5,4382732
Let's use induction:
For $n=2$, I will leave it to you to prove that
$$A^2=3A-2I$$
Now let's suppose that it's true for $n$:
$$A^n=u_nA+v_nI$$
And now we can use induction:
$$begin{align}
A^{n+1}&=A^nA\
&=(u_nA+v_nI)A\
&=u_nA^2+v_nA\
&=u_n(3A-2I)+v_nA\
&=(3u_n+v_n)A-2u_nI
end{align}$$
Can you continue the work?
answered Dec 7 at 15:31
Botond
5,4382732
answered Dec 7 at 15:31
Botond
5,4382732
answered Dec 7 at 15:31
Botond
5,4382732
answered Dec 7 at 15:31
Botond
5,4382732
5,4382732
Yuup thanks very very much
– plus plus
Dec 7 at 15:56
sorry for bothering again but how can I find the dimension of the vector field E, where , E=vect (A^(k)) , k belongs to Z
– plus plus
Dec 10 at 17:02
@plusplus Next time please make a new question. What so you mean by $text{vec}(A^k)$? Is it a vector space with basis $A^1,A^2,...$?
– Botond
Dec 10 at 17:10
Actually I thought it would be easier to continue in the same question .. I'm really sorry next time I'll do it .. yes it is a vector space with basis A^1,A^2,.. but also with( I , A^(-1) , A^(-2) .....)
– plus plus
Dec 10 at 17:13
@plusplus It's fine. First of all, can you find a basis if $k in mathbb{N}$ only?
– Botond
Dec 10 at 17:15
|
show 15 more comments
Yuup thanks very very much
– plus plus
Dec 7 at 15:56
sorry for bothering again but how can I find the dimension of the vector field E, where , E=vect (A^(k)) , k belongs to Z
– plus plus
Dec 10 at 17:02
@plusplus Next time please make a new question. What so you mean by $text{vec}(A^k)$? Is it a vector space with basis $A^1,A^2,...$?
– Botond
Dec 10 at 17:10
Actually I thought it would be easier to continue in the same question .. I'm really sorry next time I'll do it .. yes it is a vector space with basis A^1,A^2,.. but also with( I , A^(-1) , A^(-2) .....)
– plus plus
Dec 10 at 17:13
@plusplus It's fine. First of all, can you find a basis if $k in mathbb{N}$ only?
– Botond
Dec 10 at 17:15
Yuup thanks very very much
– plus plus
Dec 7 at 15:56
Yuup thanks very very much
– plus plus
Dec 7 at 15:56
sorry for bothering again but how can I find the dimension of the vector field E, where , E=vect (A^(k)) , k belongs to Z
– plus plus
Dec 10 at 17:02
sorry for bothering again but how can I find the dimension of the vector field E, where , E=vect (A^(k)) , k belongs to Z
– plus plus
Dec 10 at 17:02
@plusplus Next time please make a new question. What so you mean by $text{vec}(A^k)$? Is it a vector space with basis $A^1,A^2,...$?
– Botond
Dec 10 at 17:10
@plusplus Next time please make a new question. What so you mean by $text{vec}(A^k)$? Is it a vector space with basis $A^1,A^2,...$?
– Botond
Dec 10 at 17:10
Actually I thought it would be easier to continue in the same question .. I'm really sorry next time I'll do it .. yes it is a vector space with basis A^1,A^2,.. but also with( I , A^(-1) , A^(-2) .....)
– plus plus
Dec 10 at 17:13
Actually I thought it would be easier to continue in the same question .. I'm really sorry next time I'll do it .. yes it is a vector space with basis A^1,A^2,.. but also with( I , A^(-1) , A^(-2) .....)
– plus plus
Dec 10 at 17:13
@plusplus It's fine. First of all, can you find a basis if $k in mathbb{N}$ only?
– Botond
Dec 10 at 17:15
@plusplus It's fine. First of all, can you find a basis if $k in mathbb{N}$ only?
– Botond
Dec 10 at 17:15
|
show 15 more comments
Did you try to diagonalize $A$?
– Botond
Dec 7 at 15:07
sorry I didn't get it .. could U please give me more details
– plus plus
Dec 7 at 15:08
Can you calculate the eigenvectors and eigenvalues of $A$?
– Botond
Dec 7 at 15:11
actually not ... because we didnt talk about them in classes ..we are in a very low level yet .. but its a homework and we are not supposed to use stuff we didnt talk about it yet ... please have a look on the post again I added sth ..
– plus plus
Dec 7 at 15:15
Shouldn't $I$ be the identity matrix instead of the full $1$ matrix?
– Botond
Dec 7 at 15:25