Is there a distribution for random matrices which are constrained to have “unit vector” columns?
$begingroup$
Let $a_{ij}$ be the components of an $n times m$ random matrix of real numbers subject to the constraint that for each column $j$ we have:
$$sum_i{(a_{ij})^2}=1$$
In other words, consider a matrix whose $m$ columns are random $n$-dimensional unit vectors.
Given an $n times m$ matrix whose columns are $n$-dimensional unit vectors, is there a way to measure how different this given matrix is from a "typical" one generated using the random process described above, and how should we define "typical", is there a concept similar to standard deviation for this type of problem?
Thanks!
random-matrices
asked Dec 14 '18 at 2:08
Matt CalhounMatt Calhoun
2,9022249
$endgroup$
add a comment |
$begingroup$
Let $a_{ij}$ be the components of an $n times m$ random matrix of real numbers subject to the constraint that for each column $j$ we have:
$$sum_i{(a_{ij})^2}=1$$
In other words, consider a matrix whose $m$ columns are random $n$-dimensional unit vectors.
Given an $n times m$ matrix whose columns are $n$-dimensional unit vectors, is there a way to measure how different this given matrix is from a "typical" one generated using the random process described above, and how should we define "typical", is there a concept similar to standard deviation for this type of problem?
Thanks!
random-matrices
asked Dec 14 '18 at 2:08
Matt CalhounMatt Calhoun
2,9022249
$endgroup$
add a comment |
$begingroup$
Let $a_{ij}$ be the components of an $n times m$ random matrix of real numbers subject to the constraint that for each column $j$ we have:
$$sum_i{(a_{ij})^2}=1$$
In other words, consider a matrix whose $m$ columns are random $n$-dimensional unit vectors.
Given an $n times m$ matrix whose columns are $n$-dimensional unit vectors, is there a way to measure how different this given matrix is from a "typical" one generated using the random process described above, and how should we define "typical", is there a concept similar to standard deviation for this type of problem?
Thanks!
random-matrices
asked Dec 14 '18 at 2:08
Matt CalhounMatt Calhoun
2,9022249
$endgroup$
Let $a_{ij}$ be the components of an $n times m$ random matrix of real numbers subject to the constraint that for each column $j$ we have:
$$sum_i{(a_{ij})^2}=1$$
In other words, consider a matrix whose $m$ columns are random $n$-dimensional unit vectors.
Given an $n times m$ matrix whose columns are $n$-dimensional unit vectors, is there a way to measure how different this given matrix is from a "typical" one generated using the random process described above, and how should we define "typical", is there a concept similar to standard deviation for this type of problem?
Thanks!
random-matrices
random-matrices
asked Dec 14 '18 at 2:08
Matt CalhounMatt Calhoun
2,9022249
asked Dec 14 '18 at 2:08
Matt CalhounMatt Calhoun
2,9022249
edited Dec 14 '18 at 2:24
Matt Calhoun
asked Dec 14 '18 at 2:08
Matt CalhounMatt Calhoun
2,9022249
asked Dec 14 '18 at 2:08
Matt CalhounMatt Calhoun
2,9022249
asked Dec 14 '18 at 2:08
Matt CalhounMatt Calhoun
2,9022249
2,9022249
add a comment |
add a comment |
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