Mixing
How to transform a square orthogonal matrix into a norm-preserving non-square matrix?
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Assume we have an arbitrary $n times n$ orthogonal matrix of real values. How can you transfer such a matrix into an $m times n$ non-square matrix (where $m < n$) which also preserves the norm of any $n$ sized vector which would be multiplied by it? What would be the least computationally expensive way of doing such transformation?
linear-algebra matrices numerical-linear-algebra
asked Jan 30 at 7:23
AnonAnon
1
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add a comment |
$begingroup$
Assume we have an arbitrary $n times n$ orthogonal matrix of real values. How can you transfer such a matrix into an $m times n$ non-square matrix (where $m < n$) which also preserves the norm of any $n$ sized vector which would be multiplied by it? What would be the least computationally expensive way of doing such transformation?
linear-algebra matrices numerical-linear-algebra
asked Jan 30 at 7:23
AnonAnon
1
$endgroup$
$begingroup$
When $m<n$, there is no $mtimes n$ matrix $Ax$ such that $|Ax|=|x|$ for all $x$.
$endgroup$
– Rahul
Jan 30 at 7:38
add a comment |
$begingroup$
Assume we have an arbitrary $n times n$ orthogonal matrix of real values. How can you transfer such a matrix into an $m times n$ non-square matrix (where $m < n$) which also preserves the norm of any $n$ sized vector which would be multiplied by it? What would be the least computationally expensive way of doing such transformation?
linear-algebra matrices numerical-linear-algebra
asked Jan 30 at 7:23
AnonAnon
1
$endgroup$
Assume we have an arbitrary $n times n$ orthogonal matrix of real values. How can you transfer such a matrix into an $m times n$ non-square matrix (where $m < n$) which also preserves the norm of any $n$ sized vector which would be multiplied by it? What would be the least computationally expensive way of doing such transformation?
linear-algebra matrices numerical-linear-algebra
linear-algebra matrices numerical-linear-algebra
asked Jan 30 at 7:23
AnonAnon
1
asked Jan 30 at 7:23
AnonAnon
1
asked Jan 30 at 7:23
AnonAnon
1
asked Jan 30 at 7:23
AnonAnon
1
asked Jan 30 at 7:23
AnonAnon
1
1
$begingroup$
When $m<n$, there is no $mtimes n$ matrix $Ax$ such that $|Ax|=|x|$ for all $x$.
$endgroup$
– Rahul
Jan 30 at 7:38
add a comment |
$begingroup$
When $m<n$, there is no $mtimes n$ matrix $Ax$ such that $|Ax|=|x|$ for all $x$.
$endgroup$
– Rahul
Jan 30 at 7:38
$begingroup$
When $m<n$, there is no $mtimes n$ matrix $Ax$ such that $|Ax|=|x|$ for all $x$.
$endgroup$
– Rahul
Jan 30 at 7:38
$begingroup$
When $m<n$, there is no $mtimes n$ matrix $Ax$ such that $|Ax|=|x|$ for all $x$.
$endgroup$
– Rahul
Jan 30 at 7:38
add a comment |
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$begingroup$
When $m<n$, there is no $mtimes n$ matrix $Ax$ such that $|Ax|=|x|$ for all $x$.
$endgroup$
– Rahul
Jan 30 at 7:38