Is there a name for this matrix operation?












2












$begingroup$


Transforming a matrix by copying each element up to a certain given length ($k$) and then starting on the next row with the second element, and row after that with the third, etc. So each row is shifted by one more. For example:



$$begin{bmatrix}1\2\3\4\5end{bmatrix}
rightarrow
begin{bmatrix}1 & 2 & 3\2 & 3 & 4\3 & 4 & 5end{bmatrix}
$$



With a parameter $k=3$ or



$$begin{bmatrix}1\2\3\4\5end{bmatrix}
rightarrow
begin{bmatrix}1 & 2 & 3 & 4\2 & 3 & 4 & 5end{bmatrix}
$$



With a parameter $k=4$.






linear-algebra







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    If such operation is useful, it certainly has a name. And conversely.
    $endgroup$
    – Yves Daoust
    Dec 1 '18 at 21:05








  • 1




    $begingroup$
    Thinking to a fixed length window (length = 3 or 2 in your example) : you are sliding this window on the message "1 2 3 4 5" and you gather the results in a new matrix : thus it has something common with discrete convolution but I don't see any "closed form" matrix expression that can render this operation...
    $endgroup$
    – Jean Marie
    Dec 1 '18 at 22:15








  • 1




    $begingroup$
    I would call the 1st operation Hankelization.
    $endgroup$
    – Rodrigo de Azevedo
    Dec 2 '18 at 8:01
















2












$begingroup$


Transforming a matrix by copying each element up to a certain given length ($k$) and then starting on the next row with the second element, and row after that with the third, etc. So each row is shifted by one more. For example:



$$begin{bmatrix}1\2\3\4\5end{bmatrix}
rightarrow
begin{bmatrix}1 & 2 & 3\2 & 3 & 4\3 & 4 & 5end{bmatrix}
$$



With a parameter $k=3$ or



$$begin{bmatrix}1\2\3\4\5end{bmatrix}
rightarrow
begin{bmatrix}1 & 2 & 3 & 4\2 & 3 & 4 & 5end{bmatrix}
$$



With a parameter $k=4$.






linear-algebra







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    If such operation is useful, it certainly has a name. And conversely.
    $endgroup$
    – Yves Daoust
    Dec 1 '18 at 21:05








  • 1




    $begingroup$
    Thinking to a fixed length window (length = 3 or 2 in your example) : you are sliding this window on the message "1 2 3 4 5" and you gather the results in a new matrix : thus it has something common with discrete convolution but I don't see any "closed form" matrix expression that can render this operation...
    $endgroup$
    – Jean Marie
    Dec 1 '18 at 22:15








  • 1




    $begingroup$
    I would call the 1st operation Hankelization.
    $endgroup$
    – Rodrigo de Azevedo
    Dec 2 '18 at 8:01














2












2








2





$begingroup$


Transforming a matrix by copying each element up to a certain given length ($k$) and then starting on the next row with the second element, and row after that with the third, etc. So each row is shifted by one more. For example:



$$begin{bmatrix}1\2\3\4\5end{bmatrix}
rightarrow
begin{bmatrix}1 & 2 & 3\2 & 3 & 4\3 & 4 & 5end{bmatrix}
$$



With a parameter $k=3$ or



$$begin{bmatrix}1\2\3\4\5end{bmatrix}
rightarrow
begin{bmatrix}1 & 2 & 3 & 4\2 & 3 & 4 & 5end{bmatrix}
$$



With a parameter $k=4$.






linear-algebra







share|cite|improve this question











$endgroup$




Transforming a matrix by copying each element up to a certain given length ($k$) and then starting on the next row with the second element, and row after that with the third, etc. So each row is shifted by one more. For example:



$$begin{bmatrix}1\2\3\4\5end{bmatrix}
rightarrow
begin{bmatrix}1 & 2 & 3\2 & 3 & 4\3 & 4 & 5end{bmatrix}
$$



With a parameter $k=3$ or



$$begin{bmatrix}1\2\3\4\5end{bmatrix}
rightarrow
begin{bmatrix}1 & 2 & 3 & 4\2 & 3 & 4 & 5end{bmatrix}
$$



With a parameter $k=4$.






linear-algebra




linear-algebra






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 2 '18 at 7:38









Tianlalu

3,08121038




3,08121038










asked Dec 1 '18 at 20:49









Ken FehlingKen Fehling

1135




1135








  • 1




    $begingroup$
    If such operation is useful, it certainly has a name. And conversely.
    $endgroup$
    – Yves Daoust
    Dec 1 '18 at 21:05








  • 1




    $begingroup$
    Thinking to a fixed length window (length = 3 or 2 in your example) : you are sliding this window on the message "1 2 3 4 5" and you gather the results in a new matrix : thus it has something common with discrete convolution but I don't see any "closed form" matrix expression that can render this operation...
    $endgroup$
    – Jean Marie
    Dec 1 '18 at 22:15








  • 1




    $begingroup$
    I would call the 1st operation Hankelization.
    $endgroup$
    – Rodrigo de Azevedo
    Dec 2 '18 at 8:01














  • 1




    $begingroup$
    If such operation is useful, it certainly has a name. And conversely.
    $endgroup$
    – Yves Daoust
    Dec 1 '18 at 21:05








  • 1




    $begingroup$
    Thinking to a fixed length window (length = 3 or 2 in your example) : you are sliding this window on the message "1 2 3 4 5" and you gather the results in a new matrix : thus it has something common with discrete convolution but I don't see any "closed form" matrix expression that can render this operation...
    $endgroup$
    – Jean Marie
    Dec 1 '18 at 22:15








  • 1




    $begingroup$
    I would call the 1st operation Hankelization.
    $endgroup$
    – Rodrigo de Azevedo
    Dec 2 '18 at 8:01








1




1




$begingroup$
If such operation is useful, it certainly has a name. And conversely.
$endgroup$
– Yves Daoust
Dec 1 '18 at 21:05






$begingroup$
If such operation is useful, it certainly has a name. And conversely.
$endgroup$
– Yves Daoust
Dec 1 '18 at 21:05






1




1




$begingroup$
Thinking to a fixed length window (length = 3 or 2 in your example) : you are sliding this window on the message "1 2 3 4 5" and you gather the results in a new matrix : thus it has something common with discrete convolution but I don't see any "closed form" matrix expression that can render this operation...
$endgroup$
– Jean Marie
Dec 1 '18 at 22:15






$begingroup$
Thinking to a fixed length window (length = 3 or 2 in your example) : you are sliding this window on the message "1 2 3 4 5" and you gather the results in a new matrix : thus it has something common with discrete convolution but I don't see any "closed form" matrix expression that can render this operation...
$endgroup$
– Jean Marie
Dec 1 '18 at 22:15






1




1




$begingroup$
I would call the 1st operation Hankelization.
$endgroup$
– Rodrigo de Azevedo
Dec 2 '18 at 8:01




$begingroup$
I would call the 1st operation Hankelization.
$endgroup$
– Rodrigo de Azevedo
Dec 2 '18 at 8:01










1 Answer
1






active

oldest

votes


















1












$begingroup$

The operation looks a little too particular to me to have a (well known) name.



The resulting matrix is like a Toeplitz matrix (except that it's constant along the anti-diagonals), could be regarded as some sort of "toeplitzation" (ugh)...



For example, the second example in Matlab/Octave:



>> fliplr(toeplitz([4,5],[4,3,2,1]))

ans =



   1   2   3   4

   2   3   4   5





share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    Thanks! This opened up some good things for me to look into. From Toeplitz I found Hankel which seems like I can use to do at least something close to what I need.
    $endgroup$
    – Ken Fehling
    Dec 1 '18 at 21:43






  • 1




    $begingroup$
    If you are looking for ways to do this in Python, you may also be interested in vstack.
    $endgroup$
    – Erik André
    Dec 2 '18 at 7:56













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1 Answer
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active

oldest

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active

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active

oldest

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1












$begingroup$

The operation looks a little too particular to me to have a (well known) name.



The resulting matrix is like a Toeplitz matrix (except that it's constant along the anti-diagonals), could be regarded as some sort of "toeplitzation" (ugh)...



For example, the second example in Matlab/Octave:



>> fliplr(toeplitz([4,5],[4,3,2,1]))

ans =



   1   2   3   4

   2   3   4   5





share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    Thanks! This opened up some good things for me to look into. From Toeplitz I found Hankel which seems like I can use to do at least something close to what I need.
    $endgroup$
    – Ken Fehling
    Dec 1 '18 at 21:43






  • 1




    $begingroup$
    If you are looking for ways to do this in Python, you may also be interested in vstack.
    $endgroup$
    – Erik André
    Dec 2 '18 at 7:56


















1












$begingroup$

The operation looks a little too particular to me to have a (well known) name.



The resulting matrix is like a Toeplitz matrix (except that it's constant along the anti-diagonals), could be regarded as some sort of "toeplitzation" (ugh)...



For example, the second example in Matlab/Octave:



>> fliplr(toeplitz([4,5],[4,3,2,1]))

ans =



   1   2   3   4

   2   3   4   5





share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    Thanks! This opened up some good things for me to look into. From Toeplitz I found Hankel which seems like I can use to do at least something close to what I need.
    $endgroup$
    – Ken Fehling
    Dec 1 '18 at 21:43






  • 1




    $begingroup$
    If you are looking for ways to do this in Python, you may also be interested in vstack.
    $endgroup$
    – Erik André
    Dec 2 '18 at 7:56
















1












1








1





$begingroup$

The operation looks a little too particular to me to have a (well known) name.



The resulting matrix is like a Toeplitz matrix (except that it's constant along the anti-diagonals), could be regarded as some sort of "toeplitzation" (ugh)...



For example, the second example in Matlab/Octave:



>> fliplr(toeplitz([4,5],[4,3,2,1]))

ans =



   1   2   3   4

   2   3   4   5





share|cite|improve this answer









$endgroup$



The operation looks a little too particular to me to have a (well known) name.



The resulting matrix is like a Toeplitz matrix (except that it's constant along the anti-diagonals), could be regarded as some sort of "toeplitzation" (ugh)...



For example, the second example in Matlab/Octave:



>> fliplr(toeplitz([4,5],[4,3,2,1]))

ans =



   1   2   3   4

   2   3   4   5






share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 1 '18 at 21:25









leonbloyleonbloy

40.5k645107




40.5k645107








  • 1




    $begingroup$
    Thanks! This opened up some good things for me to look into. From Toeplitz I found Hankel which seems like I can use to do at least something close to what I need.
    $endgroup$
    – Ken Fehling
    Dec 1 '18 at 21:43






  • 1




    $begingroup$
    If you are looking for ways to do this in Python, you may also be interested in vstack.
    $endgroup$
    – Erik André
    Dec 2 '18 at 7:56
















  • 1




    $begingroup$
    Thanks! This opened up some good things for me to look into. From Toeplitz I found Hankel which seems like I can use to do at least something close to what I need.
    $endgroup$
    – Ken Fehling
    Dec 1 '18 at 21:43






  • 1




    $begingroup$
    If you are looking for ways to do this in Python, you may also be interested in vstack.
    $endgroup$
    – Erik André
    Dec 2 '18 at 7:56










1




1




$begingroup$
Thanks! This opened up some good things for me to look into. From Toeplitz I found Hankel which seems like I can use to do at least something close to what I need.
$endgroup$
– Ken Fehling
Dec 1 '18 at 21:43




$begingroup$
Thanks! This opened up some good things for me to look into. From Toeplitz I found Hankel which seems like I can use to do at least something close to what I need.
$endgroup$
– Ken Fehling
Dec 1 '18 at 21:43




1




1




$begingroup$
If you are looking for ways to do this in Python, you may also be interested in vstack.
$endgroup$
– Erik André
Dec 2 '18 at 7:56






$begingroup$
If you are looking for ways to do this in Python, you may also be interested in vstack.
$endgroup$
– Erik André
Dec 2 '18 at 7:56




















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