Determinant of a random symmetric matrix
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I am trying to determine the determinant of the following uniformly distributed random symmetric matrix $A$ with zero mean and $approx 2.9$ standard deviation.
begin{equation}
A=
begin{pmatrix}
1 & cos alpha_{12} & cos alpha_{13} & dots &cos alpha_{1N} \
cos alpha_{12}& 1 & cos alpha_{23} & dots &cos alpha_{2N} \
cos alpha_{13} & cos alpha_{23} & 1 & dots &cos alpha_{3N} \
vdots & vdots & vdots & quad & vdots \
cos alpha_{1N} & cos alpha_{2N} & cos alpha_{3N} & dots & 1\
end{pmatrix}
end{equation}
Where each vectors are linearly independent and $alpha_{ij} in [-0.5,0.5]$, for all $i,j=1,2,3,dots,N$.
Any valuable resource or help is appreciated.
linear-algebra determinant random-matrices
asked Nov 9 at 7:42
Henok 10
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Henok 10 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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up vote
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I am trying to determine the determinant of the following uniformly distributed random symmetric matrix $A$ with zero mean and $approx 2.9$ standard deviation.
begin{equation}
A=
begin{pmatrix}
1 & cos alpha_{12} & cos alpha_{13} & dots &cos alpha_{1N} \
cos alpha_{12}& 1 & cos alpha_{23} & dots &cos alpha_{2N} \
cos alpha_{13} & cos alpha_{23} & 1 & dots &cos alpha_{3N} \
vdots & vdots & vdots & quad & vdots \
cos alpha_{1N} & cos alpha_{2N} & cos alpha_{3N} & dots & 1\
end{pmatrix}
end{equation}
Where each vectors are linearly independent and $alpha_{ij} in [-0.5,0.5]$, for all $i,j=1,2,3,dots,N$.
Any valuable resource or help is appreciated.
linear-algebra determinant random-matrices
asked Nov 9 at 7:42
Henok 10
11
New contributor
Henok 10 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 9 at 7:47
1
What do you mean by "predict"?
– user10354138
Nov 9 at 7:48
You wrote symmetric matrix. Thus we should assume $alpha_{ij}=alpha_{ji}$.
– Berci
Nov 9 at 7:52
2
If you're talking about a random matrix you should specify the probability distribution for the parameters $alpha_{ij}$.
– Hans Lundmark
Nov 9 at 8:24
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am trying to determine the determinant of the following uniformly distributed random symmetric matrix $A$ with zero mean and $approx 2.9$ standard deviation.
begin{equation}
A=
begin{pmatrix}
1 & cos alpha_{12} & cos alpha_{13} & dots &cos alpha_{1N} \
cos alpha_{12}& 1 & cos alpha_{23} & dots &cos alpha_{2N} \
cos alpha_{13} & cos alpha_{23} & 1 & dots &cos alpha_{3N} \
vdots & vdots & vdots & quad & vdots \
cos alpha_{1N} & cos alpha_{2N} & cos alpha_{3N} & dots & 1\
end{pmatrix}
end{equation}
Where each vectors are linearly independent and $alpha_{ij} in [-0.5,0.5]$, for all $i,j=1,2,3,dots,N$.
Any valuable resource or help is appreciated.
linear-algebra determinant random-matrices
asked Nov 9 at 7:42
Henok 10
11
New contributor
Henok 10 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I am trying to determine the determinant of the following uniformly distributed random symmetric matrix $A$ with zero mean and $approx 2.9$ standard deviation.
begin{equation}
A=
begin{pmatrix}
1 & cos alpha_{12} & cos alpha_{13} & dots &cos alpha_{1N} \
cos alpha_{12}& 1 & cos alpha_{23} & dots &cos alpha_{2N} \
cos alpha_{13} & cos alpha_{23} & 1 & dots &cos alpha_{3N} \
vdots & vdots & vdots & quad & vdots \
cos alpha_{1N} & cos alpha_{2N} & cos alpha_{3N} & dots & 1\
end{pmatrix}
end{equation}
Where each vectors are linearly independent and $alpha_{ij} in [-0.5,0.5]$, for all $i,j=1,2,3,dots,N$.
Any valuable resource or help is appreciated.
linear-algebra determinant random-matrices
linear-algebra determinant random-matrices
asked Nov 9 at 7:42
Henok 10
11
New contributor
Henok 10 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 9 at 7:42
Henok 10
11
New contributor
Henok 10 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 13 hours ago
asked Nov 9 at 7:42
Henok 10
11
New contributor
Henok 10 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 9 at 7:42
Henok 10
11
asked Nov 9 at 7:42
Henok 10
11
11
New contributor
Henok 10 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Henok 10 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Henok 10 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 9 at 7:47
1
What do you mean by "predict"?
– user10354138
Nov 9 at 7:48
You wrote symmetric matrix. Thus we should assume $alpha_{ij}=alpha_{ji}$.
– Berci
Nov 9 at 7:52
2
If you're talking about a random matrix you should specify the probability distribution for the parameters $alpha_{ij}$.
– Hans Lundmark
Nov 9 at 8:24
add a comment |
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 9 at 7:47
1
What do you mean by "predict"?
– user10354138
Nov 9 at 7:48
You wrote symmetric matrix. Thus we should assume $alpha_{ij}=alpha_{ji}$.
– Berci
Nov 9 at 7:52
2
If you're talking about a random matrix you should specify the probability distribution for the parameters $alpha_{ij}$.
– Hans Lundmark
Nov 9 at 8:24
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 9 at 7:47
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 9 at 7:47
1
1
What do you mean by "predict"?
– user10354138
Nov 9 at 7:48
What do you mean by "predict"?
– user10354138
Nov 9 at 7:48
You wrote symmetric matrix. Thus we should assume $alpha_{ij}=alpha_{ji}$.
– Berci
Nov 9 at 7:52
You wrote symmetric matrix. Thus we should assume $alpha_{ij}=alpha_{ji}$.
– Berci
Nov 9 at 7:52
2
2
If you're talking about a random matrix you should specify the probability distribution for the parameters $alpha_{ij}$.
– Hans Lundmark
Nov 9 at 8:24
If you're talking about a random matrix you should specify the probability distribution for the parameters $alpha_{ij}$.
– Hans Lundmark
Nov 9 at 8:24
add a comment |
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Henok 10 is a new contributor. Be nice, and check out our Code of Conduct.
Henok 10 is a new contributor. Be nice, and check out our Code of Conduct.
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Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 9 at 7:47
1
What do you mean by "predict"?
– user10354138
Nov 9 at 7:48
You wrote symmetric matrix. Thus we should assume $alpha_{ij}=alpha_{ji}$.
– Berci
Nov 9 at 7:52
2
If you're talking about a random matrix you should specify the probability distribution for the parameters $alpha_{ij}$.
– Hans Lundmark
Nov 9 at 8:24