Guessing the eigenvectors knowing the eigenvalues of a 3x3 matrix Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Finding the eigenvalues of a given Markov matrixFind eigenvalues and eigenvectors of this matrixeigenvector equivalence for subspace of matrix?Finding eigenvectors of a 3x3 matrixfinding eigenvector from 3x3 matrixFinding eigenvectors of a 3x3 matrix 2Find missing Eigenvalues and check invertabilityEigenvalues and -vectors of product matrixEigenvalues and Eigenvectors in ModelsMatrix with distinct eigenvectors corresponding to eigenvalues.
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Guessing the eigenvectors knowing the eigenvalues of a 3x3 matrix
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Finding the eigenvalues of a given Markov matrixFind eigenvalues and eigenvectors of this matrixeigenvector equivalence for subspace of matrix?Finding eigenvectors of a 3x3 matrixfinding eigenvector from 3x3 matrixFinding eigenvectors of a 3x3 matrix 2Find missing Eigenvalues and check invertabilityEigenvalues and -vectors of product matrixEigenvalues and Eigenvectors in ModelsMatrix with distinct eigenvectors corresponding to eigenvalues.
$begingroup$
So I'm given a matrix $A$
$$A=beginpmatrix0.4 & 0.3& 0.3\ 0.3 & 0.5 & 0.2 \ 0.3& 0.2 & 0.5 endpmatrix$$
Find the eigenvector corresponding to the eigenvalue $lambda_1=1$ then proceed to find the remaining eigenvalues using a built in command in MatLab
So far I've found the eigenvector for $lambda_1=1$ which is $v_1=beginpmatrix1\1\1endpmatrix$ and after i've used the eig command I found the remaining eigenvalues to be $lambda_2=0.3,lambda_3=0.1$ now it wants me to literary "guess" the corresponding eigenvectors.And this is where i'm stuck. I have read lots of guides and stuff about how to find eigenvectors by inspection but that was for 2x2 matrices and for 3x3 matrices they just mentioned that they need a 3rd fact which is a bit more complicated. Besides I can't see any obvious eigenvectors.....
linear-algebra eigenvalues-eigenvectors
asked Apr 8 at 19:44
Sami ShafiSami Shafi
447
$endgroup$
add a comment |
$begingroup$
So I'm given a matrix $A$
$$A=beginpmatrix0.4 & 0.3& 0.3\ 0.3 & 0.5 & 0.2 \ 0.3& 0.2 & 0.5 endpmatrix$$
Find the eigenvector corresponding to the eigenvalue $lambda_1=1$ then proceed to find the remaining eigenvalues using a built in command in MatLab
So far I've found the eigenvector for $lambda_1=1$ which is $v_1=beginpmatrix1\1\1endpmatrix$ and after i've used the eig command I found the remaining eigenvalues to be $lambda_2=0.3,lambda_3=0.1$ now it wants me to literary "guess" the corresponding eigenvectors.And this is where i'm stuck. I have read lots of guides and stuff about how to find eigenvectors by inspection but that was for 2x2 matrices and for 3x3 matrices they just mentioned that they need a 3rd fact which is a bit more complicated. Besides I can't see any obvious eigenvectors.....
linear-algebra eigenvalues-eigenvectors
asked Apr 8 at 19:44
Sami ShafiSami Shafi
447
$endgroup$
1
$begingroup$
Where does it say "guess"? eig will give you both eigenvalues and eigenvectors.
$endgroup$
– Robert Israel
Apr 8 at 19:50
$begingroup$
@RobertIsrael In my problem sheet. (Use "eig" in matlab to find the remaining eigenvalues). From what the command returns, guess the corresponding eigenvectors then verify them (the verifying part is not an issue) but the part that it says "guess" got me pretty confused
$endgroup$
– Sami Shafi
Apr 8 at 19:55
$begingroup$
hmm maybe I've misunderstood the problem? As you said you'll get both eigenvectors and values if you use [v,b] = eig maybe it's referring to guess which one of the eigenvalues is for which eigenvectors as in you get both of them so you just somehow "see" which of them is for which?
$endgroup$
– Sami Shafi
Apr 8 at 20:00
$begingroup$
This is helpful emathhelp.net/calculators/linear-algebra/…
$endgroup$
– amitava
Apr 8 at 20:55
add a comment |
$begingroup$
So I'm given a matrix $A$
$$A=beginpmatrix0.4 & 0.3& 0.3\ 0.3 & 0.5 & 0.2 \ 0.3& 0.2 & 0.5 endpmatrix$$
Find the eigenvector corresponding to the eigenvalue $lambda_1=1$ then proceed to find the remaining eigenvalues using a built in command in MatLab
So far I've found the eigenvector for $lambda_1=1$ which is $v_1=beginpmatrix1\1\1endpmatrix$ and after i've used the eig command I found the remaining eigenvalues to be $lambda_2=0.3,lambda_3=0.1$ now it wants me to literary "guess" the corresponding eigenvectors.And this is where i'm stuck. I have read lots of guides and stuff about how to find eigenvectors by inspection but that was for 2x2 matrices and for 3x3 matrices they just mentioned that they need a 3rd fact which is a bit more complicated. Besides I can't see any obvious eigenvectors.....
linear-algebra eigenvalues-eigenvectors
asked Apr 8 at 19:44
Sami ShafiSami Shafi
447
$endgroup$
So I'm given a matrix $A$
$$A=beginpmatrix0.4 & 0.3& 0.3\ 0.3 & 0.5 & 0.2 \ 0.3& 0.2 & 0.5 endpmatrix$$
Find the eigenvector corresponding to the eigenvalue $lambda_1=1$ then proceed to find the remaining eigenvalues using a built in command in MatLab
So far I've found the eigenvector for $lambda_1=1$ which is $v_1=beginpmatrix1\1\1endpmatrix$ and after i've used the eig command I found the remaining eigenvalues to be $lambda_2=0.3,lambda_3=0.1$ now it wants me to literary "guess" the corresponding eigenvectors.And this is where i'm stuck. I have read lots of guides and stuff about how to find eigenvectors by inspection but that was for 2x2 matrices and for 3x3 matrices they just mentioned that they need a 3rd fact which is a bit more complicated. Besides I can't see any obvious eigenvectors.....
linear-algebra eigenvalues-eigenvectors
linear-algebra eigenvalues-eigenvectors
asked Apr 8 at 19:44
Sami ShafiSami Shafi
447
asked Apr 8 at 19:44
Sami ShafiSami Shafi
447
asked Apr 8 at 19:44
Sami ShafiSami Shafi
447
asked Apr 8 at 19:44
Sami ShafiSami Shafi
447
asked Apr 8 at 19:44
Sami ShafiSami Shafi
447
447
1
$begingroup$
Where does it say "guess"? eig will give you both eigenvalues and eigenvectors.
$endgroup$
– Robert Israel
Apr 8 at 19:50
$begingroup$
@RobertIsrael In my problem sheet. (Use "eig" in matlab to find the remaining eigenvalues). From what the command returns, guess the corresponding eigenvectors then verify them (the verifying part is not an issue) but the part that it says "guess" got me pretty confused
$endgroup$
– Sami Shafi
Apr 8 at 19:55
$begingroup$
hmm maybe I've misunderstood the problem? As you said you'll get both eigenvectors and values if you use [v,b] = eig maybe it's referring to guess which one of the eigenvalues is for which eigenvectors as in you get both of them so you just somehow "see" which of them is for which?
$endgroup$
– Sami Shafi
Apr 8 at 20:00
$begingroup$
This is helpful emathhelp.net/calculators/linear-algebra/…
$endgroup$
– amitava
Apr 8 at 20:55
add a comment |
1
$begingroup$
Where does it say "guess"? eig will give you both eigenvalues and eigenvectors.
$endgroup$
– Robert Israel
Apr 8 at 19:50
$begingroup$
@RobertIsrael In my problem sheet. (Use "eig" in matlab to find the remaining eigenvalues). From what the command returns, guess the corresponding eigenvectors then verify them (the verifying part is not an issue) but the part that it says "guess" got me pretty confused
$endgroup$
– Sami Shafi
Apr 8 at 19:55
$begingroup$
hmm maybe I've misunderstood the problem? As you said you'll get both eigenvectors and values if you use [v,b] = eig maybe it's referring to guess which one of the eigenvalues is for which eigenvectors as in you get both of them so you just somehow "see" which of them is for which?
$endgroup$
– Sami Shafi
Apr 8 at 20:00
$begingroup$
This is helpful emathhelp.net/calculators/linear-algebra/…
$endgroup$
– amitava
Apr 8 at 20:55
1
1
$begingroup$
Where does it say "guess"? eig will give you both eigenvalues and eigenvectors.
$endgroup$
– Robert Israel
Apr 8 at 19:50
$begingroup$
Where does it say "guess"? eig will give you both eigenvalues and eigenvectors.
$endgroup$
– Robert Israel
Apr 8 at 19:50
$begingroup$
@RobertIsrael In my problem sheet. (Use "eig" in matlab to find the remaining eigenvalues). From what the command returns, guess the corresponding eigenvectors then verify them (the verifying part is not an issue) but the part that it says "guess" got me pretty confused
$endgroup$
– Sami Shafi
Apr 8 at 19:55
$begingroup$
@RobertIsrael In my problem sheet. (Use "eig" in matlab to find the remaining eigenvalues). From what the command returns, guess the corresponding eigenvectors then verify them (the verifying part is not an issue) but the part that it says "guess" got me pretty confused
$endgroup$
– Sami Shafi
Apr 8 at 19:55
$begingroup$
hmm maybe I've misunderstood the problem? As you said you'll get both eigenvectors and values if you use [v,b] = eig maybe it's referring to guess which one of the eigenvalues is for which eigenvectors as in you get both of them so you just somehow "see" which of them is for which?
$endgroup$
– Sami Shafi
Apr 8 at 20:00
$begingroup$
hmm maybe I've misunderstood the problem? As you said you'll get both eigenvectors and values if you use [v,b] = eig maybe it's referring to guess which one of the eigenvalues is for which eigenvectors as in you get both of them so you just somehow "see" which of them is for which?
$endgroup$
– Sami Shafi
Apr 8 at 20:00
$begingroup$
This is helpful emathhelp.net/calculators/linear-algebra/…
$endgroup$
– amitava
Apr 8 at 20:55
$begingroup$
This is helpful emathhelp.net/calculators/linear-algebra/…
$endgroup$
– amitava
Apr 8 at 20:55
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Not really "guesses", but...
Note that $$A - 0.3 I = pmatrix0.1 & 0.3 & 0.3cr
0.3 & 0.2 & 0.2cr
0.3 & 0.2 & 0.2cr $$
has its second and third columns equal. That says that $pmatrix0cr 1 cr -1cr$ will be in its null space, i.e. an eigenvector of $A$ for eigenvalue $0.3$.
Now $A$ being a symmetric matrix, its eigenvectors are orthogonal, so the eigenvector for
the remaining eigenvalue $0.1$ has sum $0$ and its second and third entries equal. Thus
it should be (a multiple of) $pmatrix2 cr -1cr -1cr$.
answered Apr 9 at 3:45
Robert IsraelRobert Israel
331k23221478
$endgroup$
add a comment |
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$begingroup$
Not really "guesses", but...
Note that $$A - 0.3 I = pmatrix0.1 & 0.3 & 0.3cr
0.3 & 0.2 & 0.2cr
0.3 & 0.2 & 0.2cr $$
has its second and third columns equal. That says that $pmatrix0cr 1 cr -1cr$ will be in its null space, i.e. an eigenvector of $A$ for eigenvalue $0.3$.
Now $A$ being a symmetric matrix, its eigenvectors are orthogonal, so the eigenvector for
the remaining eigenvalue $0.1$ has sum $0$ and its second and third entries equal. Thus
it should be (a multiple of) $pmatrix2 cr -1cr -1cr$.
answered Apr 9 at 3:45
Robert IsraelRobert Israel
331k23221478
$endgroup$
add a comment |
$begingroup$
Not really "guesses", but...
Note that $$A - 0.3 I = pmatrix0.1 & 0.3 & 0.3cr
0.3 & 0.2 & 0.2cr
0.3 & 0.2 & 0.2cr $$
has its second and third columns equal. That says that $pmatrix0cr 1 cr -1cr$ will be in its null space, i.e. an eigenvector of $A$ for eigenvalue $0.3$.
Now $A$ being a symmetric matrix, its eigenvectors are orthogonal, so the eigenvector for
the remaining eigenvalue $0.1$ has sum $0$ and its second and third entries equal. Thus
it should be (a multiple of) $pmatrix2 cr -1cr -1cr$.
answered Apr 9 at 3:45
Robert IsraelRobert Israel
331k23221478
$endgroup$
add a comment |
$begingroup$
Not really "guesses", but...
Note that $$A - 0.3 I = pmatrix0.1 & 0.3 & 0.3cr
0.3 & 0.2 & 0.2cr
0.3 & 0.2 & 0.2cr $$
has its second and third columns equal. That says that $pmatrix0cr 1 cr -1cr$ will be in its null space, i.e. an eigenvector of $A$ for eigenvalue $0.3$.
Now $A$ being a symmetric matrix, its eigenvectors are orthogonal, so the eigenvector for
the remaining eigenvalue $0.1$ has sum $0$ and its second and third entries equal. Thus
it should be (a multiple of) $pmatrix2 cr -1cr -1cr$.
answered Apr 9 at 3:45
Robert IsraelRobert Israel
331k23221478
$endgroup$
Not really "guesses", but...
Note that $$A - 0.3 I = pmatrix0.1 & 0.3 & 0.3cr
0.3 & 0.2 & 0.2cr
0.3 & 0.2 & 0.2cr $$
has its second and third columns equal. That says that $pmatrix0cr 1 cr -1cr$ will be in its null space, i.e. an eigenvector of $A$ for eigenvalue $0.3$.
Now $A$ being a symmetric matrix, its eigenvectors are orthogonal, so the eigenvector for
the remaining eigenvalue $0.1$ has sum $0$ and its second and third entries equal. Thus
it should be (a multiple of) $pmatrix2 cr -1cr -1cr$.
answered Apr 9 at 3:45
Robert IsraelRobert Israel
331k23221478
answered Apr 9 at 3:45
Robert IsraelRobert Israel
331k23221478
answered Apr 9 at 3:45
Robert IsraelRobert Israel
331k23221478
answered Apr 9 at 3:45
Robert IsraelRobert Israel
331k23221478
331k23221478
add a comment |
add a comment |
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1
$begingroup$
Where does it say "guess"? eig will give you both eigenvalues and eigenvectors.
$endgroup$
– Robert Israel
Apr 8 at 19:50
$begingroup$
@RobertIsrael In my problem sheet. (Use "eig" in matlab to find the remaining eigenvalues). From what the command returns, guess the corresponding eigenvectors then verify them (the verifying part is not an issue) but the part that it says "guess" got me pretty confused
$endgroup$
– Sami Shafi
Apr 8 at 19:55
$begingroup$
hmm maybe I've misunderstood the problem? As you said you'll get both eigenvectors and values if you use [v,b] = eig maybe it's referring to guess which one of the eigenvalues is for which eigenvectors as in you get both of them so you just somehow "see" which of them is for which?
$endgroup$
– Sami Shafi
Apr 8 at 20:00
$begingroup$
This is helpful emathhelp.net/calculators/linear-algebra/…
$endgroup$
– amitava
Apr 8 at 20:55