If $L,A in m(n,n)$ on $R$, when exists L for which $(L^{T}AL)$ is a diagonal block matrix?
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If $L,A in m(n,n)$ on $R$, when exists L for which $(L^{T}AL)$ is a diagonal block matrix? Of course if $A$ is symmetrycal then $L$ exists and is a matrix of its eigenvectors, but I don't want to consider this case.
linear-algebra
asked Dec 16 '18 at 13:01
LandauLandau
447
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0
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If $L,A in m(n,n)$ on $R$, when exists L for which $(L^{T}AL)$ is a diagonal block matrix? Of course if $A$ is symmetrycal then $L$ exists and is a matrix of its eigenvectors, but I don't want to consider this case.
linear-algebra
asked Dec 16 '18 at 13:01
LandauLandau
447
$endgroup$
$begingroup$
You are going to need a stronger condition to make this interesting, because every $ntimes n$ matrix is a diagonal block matrix with one $ntimes n$ block.
$endgroup$
– Aaron
Dec 16 '18 at 13:18
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It was implicit that the numbers of blocks must be more than one. @Aaron
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– Landau
Dec 16 '18 at 13:24
add a comment |
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$begingroup$
If $L,A in m(n,n)$ on $R$, when exists L for which $(L^{T}AL)$ is a diagonal block matrix? Of course if $A$ is symmetrycal then $L$ exists and is a matrix of its eigenvectors, but I don't want to consider this case.
linear-algebra
asked Dec 16 '18 at 13:01
LandauLandau
447
$endgroup$
If $L,A in m(n,n)$ on $R$, when exists L for which $(L^{T}AL)$ is a diagonal block matrix? Of course if $A$ is symmetrycal then $L$ exists and is a matrix of its eigenvectors, but I don't want to consider this case.
linear-algebra
linear-algebra
asked Dec 16 '18 at 13:01
LandauLandau
447
asked Dec 16 '18 at 13:01
LandauLandau
447
asked Dec 16 '18 at 13:01
LandauLandau
447
asked Dec 16 '18 at 13:01
LandauLandau
447
asked Dec 16 '18 at 13:01
LandauLandau
447
447
$begingroup$
You are going to need a stronger condition to make this interesting, because every $ntimes n$ matrix is a diagonal block matrix with one $ntimes n$ block.
$endgroup$
– Aaron
Dec 16 '18 at 13:18
$begingroup$
It was implicit that the numbers of blocks must be more than one. @Aaron
$endgroup$
– Landau
Dec 16 '18 at 13:24
add a comment |
$begingroup$
You are going to need a stronger condition to make this interesting, because every $ntimes n$ matrix is a diagonal block matrix with one $ntimes n$ block.
$endgroup$
– Aaron
Dec 16 '18 at 13:18
$begingroup$
It was implicit that the numbers of blocks must be more than one. @Aaron
$endgroup$
– Landau
Dec 16 '18 at 13:24
$begingroup$
You are going to need a stronger condition to make this interesting, because every $ntimes n$ matrix is a diagonal block matrix with one $ntimes n$ block.
$endgroup$
– Aaron
Dec 16 '18 at 13:18
$begingroup$
You are going to need a stronger condition to make this interesting, because every $ntimes n$ matrix is a diagonal block matrix with one $ntimes n$ block.
$endgroup$
– Aaron
Dec 16 '18 at 13:18
$begingroup$
It was implicit that the numbers of blocks must be more than one. @Aaron
$endgroup$
– Landau
Dec 16 '18 at 13:24
$begingroup$
It was implicit that the numbers of blocks must be more than one. @Aaron
$endgroup$
– Landau
Dec 16 '18 at 13:24
add a comment |
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$begingroup$
You are going to need a stronger condition to make this interesting, because every $ntimes n$ matrix is a diagonal block matrix with one $ntimes n$ block.
$endgroup$
– Aaron
Dec 16 '18 at 13:18
$begingroup$
It was implicit that the numbers of blocks must be more than one. @Aaron
$endgroup$
– Landau
Dec 16 '18 at 13:24