Band matrix conjugation relation between orthogonal matrices
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Suppose I have two orthogonal matrices:
$C_1,C_2$ of some dimension $n$.
It is given that
$C_2 = R_1*C_1*R_2$
where R1,R2 are orthogonal matrices as well.
How can I solve for $R_1$ and $R_2$ when $C_1,C_2$ are given?
Additionally, if it is given that $R_1$ and $R_2$ are band matrices,
do I have a way to promote a solution, such that $R_1$ and $R_2$ will be band matrices?
For a definition of band matrix:
https://en.wikipedia.org/wiki/Band_matrix
matrices matrix-decomposition orthogonal-matrices
asked Jan 19 at 5:12
Day_DreamerDay_Dreamer
1013
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add a comment |
$begingroup$
Suppose I have two orthogonal matrices:
$C_1,C_2$ of some dimension $n$.
It is given that
$C_2 = R_1*C_1*R_2$
where R1,R2 are orthogonal matrices as well.
How can I solve for $R_1$ and $R_2$ when $C_1,C_2$ are given?
Additionally, if it is given that $R_1$ and $R_2$ are band matrices,
do I have a way to promote a solution, such that $R_1$ and $R_2$ will be band matrices?
For a definition of band matrix:
https://en.wikipedia.org/wiki/Band_matrix
matrices matrix-decomposition orthogonal-matrices
asked Jan 19 at 5:12
Day_DreamerDay_Dreamer
1013
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Welcome to Mathematics Stack Exchange! Take the short tour to see how how to get the most from your time here.
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– dantopa
Jan 19 at 5:29
add a comment |
$begingroup$
Suppose I have two orthogonal matrices:
$C_1,C_2$ of some dimension $n$.
It is given that
$C_2 = R_1*C_1*R_2$
where R1,R2 are orthogonal matrices as well.
How can I solve for $R_1$ and $R_2$ when $C_1,C_2$ are given?
Additionally, if it is given that $R_1$ and $R_2$ are band matrices,
do I have a way to promote a solution, such that $R_1$ and $R_2$ will be band matrices?
For a definition of band matrix:
https://en.wikipedia.org/wiki/Band_matrix
matrices matrix-decomposition orthogonal-matrices
asked Jan 19 at 5:12
Day_DreamerDay_Dreamer
1013
$endgroup$
Suppose I have two orthogonal matrices:
$C_1,C_2$ of some dimension $n$.
It is given that
$C_2 = R_1*C_1*R_2$
where R1,R2 are orthogonal matrices as well.
How can I solve for $R_1$ and $R_2$ when $C_1,C_2$ are given?
Additionally, if it is given that $R_1$ and $R_2$ are band matrices,
do I have a way to promote a solution, such that $R_1$ and $R_2$ will be band matrices?
For a definition of band matrix:
https://en.wikipedia.org/wiki/Band_matrix
matrices matrix-decomposition orthogonal-matrices
matrices matrix-decomposition orthogonal-matrices
asked Jan 19 at 5:12
Day_DreamerDay_Dreamer
1013
asked Jan 19 at 5:12
Day_DreamerDay_Dreamer
1013
edited Jan 19 at 6:44
Day_Dreamer
asked Jan 19 at 5:12
Day_DreamerDay_Dreamer
1013
asked Jan 19 at 5:12
Day_DreamerDay_Dreamer
1013
asked Jan 19 at 5:12
Day_DreamerDay_Dreamer
1013
1013
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– dantopa
Jan 19 at 5:29
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– dantopa
Jan 19 at 5:29
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Welcome to Mathematics Stack Exchange! Take the short tour to see how how to get the most from your time here.
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– dantopa
Jan 19 at 5:29
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– dantopa
Jan 19 at 5:29
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– dantopa
Jan 19 at 5:29