Eigenvalues and eigenvectors of a matrix-transformationFind the associated matrix of a linear transformationFind eigenvalues and eigenvectors: strange caseEigenvalues and Eigenvectors Diagonilizationfind eigenvalues and eigenvectorsFind eigenvalues and eigenvectors of this matrixFind the eigenvalues and associated eigenvectors for this matrixCalculating eigenvalues and eigenvectorslinear transformation eigenvectors and eigenvaluesfind the eigenvalues and eigenvectors of the reflection matrix.Eigenvalues and eigenvectors of a Block Tridiagonal MatrixEigenvectors and eigenvalues of the zero matrix
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Eigenvalues and eigenvectors of a matrix-transformation
Find the associated matrix of a linear transformationFind eigenvalues and eigenvectors: strange caseEigenvalues and Eigenvectors Diagonilizationfind eigenvalues and eigenvectorsFind eigenvalues and eigenvectors of this matrixFind the eigenvalues and associated eigenvectors for this matrixCalculating eigenvalues and eigenvectorslinear transformation eigenvectors and eigenvaluesfind the eigenvalues and eigenvectors of the reflection matrix.Eigenvalues and eigenvectors of a Block Tridiagonal MatrixEigenvectors and eigenvalues of the zero matrix
$begingroup$
If we have the linear operator: $Tbeginpmatrix
a & b \
c & d \
endpmatrix$ = $beginpmatrix
2c & a+c \
b-2c & d \
endpmatrix$
How would I find the eigenvalues and eigenvectors?
What I was trying to do was making the $$detleft(lambda I- beginpmatrix
2c & a+c \
b-2c & d \
endpmatrixright)$$ But somehow I feel this is wrong, how can I do it?
linear-algebra linear-transformations
edited Mar 21 at 17:52
Brian
1,268216
asked Mar 21 at 17:47
Juju9704Juju9704
34511
$endgroup$
add a comment |
$begingroup$
If we have the linear operator: $Tbeginpmatrix
a & b \
c & d \
endpmatrix$ = $beginpmatrix
2c & a+c \
b-2c & d \
endpmatrix$
How would I find the eigenvalues and eigenvectors?
What I was trying to do was making the $$detleft(lambda I- beginpmatrix
2c & a+c \
b-2c & d \
endpmatrixright)$$ But somehow I feel this is wrong, how can I do it?
linear-algebra linear-transformations
edited Mar 21 at 17:52
Brian
1,268216
asked Mar 21 at 17:47
Juju9704Juju9704
34511
$endgroup$
1
$begingroup$
Are we doing your homework?
$endgroup$
– Maria Mazur
Mar 21 at 17:54
$begingroup$
$beginbmatrix 2c & a+c \ b-2c & d \ endbmatrix$ is not the matrix of $T$. Assume $T=beginbmatrixp&q\r&s\endbmatrix$ and find $p,q,r,s$ using the description of $T$ given.
$endgroup$
– Shubham Johri
Mar 21 at 17:55
$begingroup$
Hahaha not my homework, I am introducing myself to eigenvalues
$endgroup$
– Juju9704
Mar 21 at 17:57
1
$begingroup$
4 questions in 3 hours. Take time to breath...
$endgroup$
– Jean Marie
Mar 21 at 22:30
add a comment |
$begingroup$
If we have the linear operator: $Tbeginpmatrix
a & b \
c & d \
endpmatrix$ = $beginpmatrix
2c & a+c \
b-2c & d \
endpmatrix$
How would I find the eigenvalues and eigenvectors?
What I was trying to do was making the $$detleft(lambda I- beginpmatrix
2c & a+c \
b-2c & d \
endpmatrixright)$$ But somehow I feel this is wrong, how can I do it?
linear-algebra linear-transformations
edited Mar 21 at 17:52
Brian
1,268216
asked Mar 21 at 17:47
Juju9704Juju9704
34511
$endgroup$
If we have the linear operator: $Tbeginpmatrix
a & b \
c & d \
endpmatrix$ = $beginpmatrix
2c & a+c \
b-2c & d \
endpmatrix$
How would I find the eigenvalues and eigenvectors?
What I was trying to do was making the $$detleft(lambda I- beginpmatrix
2c & a+c \
b-2c & d \
endpmatrixright)$$ But somehow I feel this is wrong, how can I do it?
linear-algebra linear-transformations
linear-algebra linear-transformations
edited Mar 21 at 17:52
Brian
1,268216
asked Mar 21 at 17:47
Juju9704Juju9704
34511
edited Mar 21 at 17:52
Brian
1,268216
asked Mar 21 at 17:47
Juju9704Juju9704
34511
edited Mar 21 at 17:52
Brian
1,268216
edited Mar 21 at 17:52
Brian
1,268216
edited Mar 21 at 17:52
Brian
1,268216
1,268216
asked Mar 21 at 17:47
Juju9704Juju9704
34511
asked Mar 21 at 17:47
Juju9704Juju9704
34511
asked Mar 21 at 17:47
Juju9704Juju9704
34511
34511
1
$begingroup$
Are we doing your homework?
$endgroup$
– Maria Mazur
Mar 21 at 17:54
$begingroup$
$beginbmatrix 2c & a+c \ b-2c & d \ endbmatrix$ is not the matrix of $T$. Assume $T=beginbmatrixp&q\r&s\endbmatrix$ and find $p,q,r,s$ using the description of $T$ given.
$endgroup$
– Shubham Johri
Mar 21 at 17:55
$begingroup$
Hahaha not my homework, I am introducing myself to eigenvalues
$endgroup$
– Juju9704
Mar 21 at 17:57
1
$begingroup$
4 questions in 3 hours. Take time to breath...
$endgroup$
– Jean Marie
Mar 21 at 22:30
add a comment |
1
$begingroup$
Are we doing your homework?
$endgroup$
– Maria Mazur
Mar 21 at 17:54
$begingroup$
$beginbmatrix 2c & a+c \ b-2c & d \ endbmatrix$ is not the matrix of $T$. Assume $T=beginbmatrixp&q\r&s\endbmatrix$ and find $p,q,r,s$ using the description of $T$ given.
$endgroup$
– Shubham Johri
Mar 21 at 17:55
$begingroup$
Hahaha not my homework, I am introducing myself to eigenvalues
$endgroup$
– Juju9704
Mar 21 at 17:57
1
$begingroup$
4 questions in 3 hours. Take time to breath...
$endgroup$
– Jean Marie
Mar 21 at 22:30
1
1
$begingroup$
Are we doing your homework?
$endgroup$
– Maria Mazur
Mar 21 at 17:54
$begingroup$
Are we doing your homework?
$endgroup$
– Maria Mazur
Mar 21 at 17:54
$begingroup$
$beginbmatrix 2c & a+c \ b-2c & d \ endbmatrix$ is not the matrix of $T$. Assume $T=beginbmatrixp&q\r&s\endbmatrix$ and find $p,q,r,s$ using the description of $T$ given.
$endgroup$
– Shubham Johri
Mar 21 at 17:55
$begingroup$
$beginbmatrix 2c & a+c \ b-2c & d \ endbmatrix$ is not the matrix of $T$. Assume $T=beginbmatrixp&q\r&s\endbmatrix$ and find $p,q,r,s$ using the description of $T$ given.
$endgroup$
– Shubham Johri
Mar 21 at 17:55
$begingroup$
Hahaha not my homework, I am introducing myself to eigenvalues
$endgroup$
– Juju9704
Mar 21 at 17:57
$begingroup$
Hahaha not my homework, I am introducing myself to eigenvalues
$endgroup$
– Juju9704
Mar 21 at 17:57
1
1
$begingroup$
4 questions in 3 hours. Take time to breath...
$endgroup$
– Jean Marie
Mar 21 at 22:30
$begingroup$
4 questions in 3 hours. Take time to breath...
$endgroup$
– Jean Marie
Mar 21 at 22:30
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
There is no use of the matrix structure, meaning we can decide on an order as long as we stay consistent:
$$
T
left(
beginarrayc
a \
b \
c \
d
endarray
right) =
left(
beginarrayc
2c \
a+c \
b-2c \
d
endarray
right)
$$
In turn, there is a 4 by 4 matrix that accomplishes this. Find it and its eigenvalues
This is the same idea as for polynomials of degree no larger than some $k.$ It is a matter of being careful about picking a basis (not necessarily writing it out) and writing in that basis.
answered Mar 21 at 17:54
Will JagyWill Jagy
104k5102201
$endgroup$
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
There is no use of the matrix structure, meaning we can decide on an order as long as we stay consistent:
$$
T
left(
beginarrayc
a \
b \
c \
d
endarray
right) =
left(
beginarrayc
2c \
a+c \
b-2c \
d
endarray
right)
$$
In turn, there is a 4 by 4 matrix that accomplishes this. Find it and its eigenvalues
This is the same idea as for polynomials of degree no larger than some $k.$ It is a matter of being careful about picking a basis (not necessarily writing it out) and writing in that basis.
answered Mar 21 at 17:54
Will JagyWill Jagy
104k5102201
$endgroup$
add a comment |
$begingroup$
There is no use of the matrix structure, meaning we can decide on an order as long as we stay consistent:
$$
T
left(
beginarrayc
a \
b \
c \
d
endarray
right) =
left(
beginarrayc
2c \
a+c \
b-2c \
d
endarray
right)
$$
In turn, there is a 4 by 4 matrix that accomplishes this. Find it and its eigenvalues
This is the same idea as for polynomials of degree no larger than some $k.$ It is a matter of being careful about picking a basis (not necessarily writing it out) and writing in that basis.
answered Mar 21 at 17:54
Will JagyWill Jagy
104k5102201
$endgroup$
add a comment |
$begingroup$
There is no use of the matrix structure, meaning we can decide on an order as long as we stay consistent:
$$
T
left(
beginarrayc
a \
b \
c \
d
endarray
right) =
left(
beginarrayc
2c \
a+c \
b-2c \
d
endarray
right)
$$
In turn, there is a 4 by 4 matrix that accomplishes this. Find it and its eigenvalues
This is the same idea as for polynomials of degree no larger than some $k.$ It is a matter of being careful about picking a basis (not necessarily writing it out) and writing in that basis.
answered Mar 21 at 17:54
Will JagyWill Jagy
104k5102201
$endgroup$
There is no use of the matrix structure, meaning we can decide on an order as long as we stay consistent:
$$
T
left(
beginarrayc
a \
b \
c \
d
endarray
right) =
left(
beginarrayc
2c \
a+c \
b-2c \
d
endarray
right)
$$
In turn, there is a 4 by 4 matrix that accomplishes this. Find it and its eigenvalues
This is the same idea as for polynomials of degree no larger than some $k.$ It is a matter of being careful about picking a basis (not necessarily writing it out) and writing in that basis.
answered Mar 21 at 17:54
Will JagyWill Jagy
104k5102201
answered Mar 21 at 17:54
Will JagyWill Jagy
104k5102201
answered Mar 21 at 17:54
Will JagyWill Jagy
104k5102201
answered Mar 21 at 17:54
Will JagyWill Jagy
104k5102201
104k5102201
add a comment |
add a comment |
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1
$begingroup$
Are we doing your homework?
$endgroup$
– Maria Mazur
Mar 21 at 17:54
$begingroup$
$beginbmatrix 2c & a+c \ b-2c & d \ endbmatrix$ is not the matrix of $T$. Assume $T=beginbmatrixp&q\r&s\endbmatrix$ and find $p,q,r,s$ using the description of $T$ given.
$endgroup$
– Shubham Johri
Mar 21 at 17:55
$begingroup$
Hahaha not my homework, I am introducing myself to eigenvalues
$endgroup$
– Juju9704
Mar 21 at 17:57
1
$begingroup$
4 questions in 3 hours. Take time to breath...
$endgroup$
– Jean Marie
Mar 21 at 22:30