Can we get the derivative of a Toeplitz function?

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Like 'Toeplitz(c,r)', which means a Toeplitz matrix formed by a column vector 'c' and a row vector 'r'. Can we get the derivatives of this function?



Like $fracpartialtextToeplitz(c,r)partial c$?




derivatives matrix-calculus




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  • It sounds very weird to call this a "Toeplitz function".
    – Cave Johnson
    Jul 24 at 20:57














up vote
0
down vote

favorite
1












Like 'Toeplitz(c,r)', which means a Toeplitz matrix formed by a column vector 'c' and a row vector 'r'. Can we get the derivatives of this function?



Like $fracpartialtextToeplitz(c,r)partial c$?




derivatives matrix-calculus




share|cite|improve this question



















  • It sounds very weird to call this a "Toeplitz function".
    – Cave Johnson
    Jul 24 at 20:57












up vote
0
down vote

favorite
1









up vote
0
down vote

favorite
1






1





Like 'Toeplitz(c,r)', which means a Toeplitz matrix formed by a column vector 'c' and a row vector 'r'. Can we get the derivatives of this function?



Like $fracpartialtextToeplitz(c,r)partial c$?




derivatives matrix-calculus




share|cite|improve this question











Like 'Toeplitz(c,r)', which means a Toeplitz matrix formed by a column vector 'c' and a row vector 'r'. Can we get the derivatives of this function?



Like $fracpartialtextToeplitz(c,r)partial c$?





derivatives matrix-calculus





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 24 at 4:13









J L

112




112











  • It sounds very weird to call this a "Toeplitz function".
    – Cave Johnson
    Jul 24 at 20:57
















  • It sounds very weird to call this a "Toeplitz function".
    – Cave Johnson
    Jul 24 at 20:57















It sounds very weird to call this a "Toeplitz function".
– Cave Johnson
Jul 24 at 20:57




It sounds very weird to call this a "Toeplitz function".
– Cave Johnson
Jul 24 at 20:57










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Well, if your Toeplitz matrix is given by the function
$$eqalign
T &= rm Toeplitz(c,r) cr
$$
then its gradient with respect to the $k^th$ component of the $c$ vector is the matrix
$$eqalign
fracpartial Tpartial c_k &= rm Toeplitz(e_k,0) cr
$$
where $e_k$ is the $k^th$ vector of the standard cartesian basis.






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    Well, if your Toeplitz matrix is given by the function
    $$eqalign
    T &= rm Toeplitz(c,r) cr
    $$
    then its gradient with respect to the $k^th$ component of the $c$ vector is the matrix
    $$eqalign
    fracpartial Tpartial c_k &= rm Toeplitz(e_k,0) cr
    $$
    where $e_k$ is the $k^th$ vector of the standard cartesian basis.






    share|cite|improve this answer



























      up vote
      0
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      Well, if your Toeplitz matrix is given by the function
      $$eqalign
      T &= rm Toeplitz(c,r) cr
      $$
      then its gradient with respect to the $k^th$ component of the $c$ vector is the matrix
      $$eqalign
      fracpartial Tpartial c_k &= rm Toeplitz(e_k,0) cr
      $$
      where $e_k$ is the $k^th$ vector of the standard cartesian basis.






      share|cite|improve this answer

























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        up vote
        0
        down vote









        Well, if your Toeplitz matrix is given by the function
        $$eqalign
        T &= rm Toeplitz(c,r) cr
        $$
        then its gradient with respect to the $k^th$ component of the $c$ vector is the matrix
        $$eqalign
        fracpartial Tpartial c_k &= rm Toeplitz(e_k,0) cr
        $$
        where $e_k$ is the $k^th$ vector of the standard cartesian basis.






        share|cite|improve this answer















        Well, if your Toeplitz matrix is given by the function
        $$eqalign
        T &= rm Toeplitz(c,r) cr
        $$
        then its gradient with respect to the $k^th$ component of the $c$ vector is the matrix
        $$eqalign
        fracpartial Tpartial c_k &= rm Toeplitz(e_k,0) cr
        $$
        where $e_k$ is the $k^th$ vector of the standard cartesian basis.







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        share|cite|improve this answer



        share|cite|improve this answer








        edited Jul 24 at 22:31


























        answered Jul 24 at 20:53









        greg

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