Given a mathematical formula or definition, how to find how is it called and where to find the mathematical...
$begingroup$
I am trying to solve a certain physical problem. I found a way to express the problem as one of solving the following system of equations:
$$begin{pmatrix}A_{s1}\
A_{s2}
end{pmatrix}=begin{pmatrix}f_{11}(d_{1},d_{2},d_{3},d_{4}) & f_{12}(d_{1},d_{2},d_{3},d_{4})\
f_{21}(d_{1},d_{2},d_{3},d_{4}) & f_{22}(d_{1},d_{2},d_{3},d_{4})
end{pmatrix}begin{pmatrix}A_{m1}\
A_{m2}
end{pmatrix}$$
where $A_{mj}$ and $f_{jk}$ are known; and $d_n$ are unknown but constrained to a finite volume of $ℝ^4$.
I wish to solve simultaneously for $A_{sj}$ and $d_n$. Intuition tells me that for the specific form of the $f_{jk}$ functions actually used in the problem, there is a finite or at most countably infinite number of solutions.
What I am asking in this question is for pointers to the mathematical theory which covers this kind of problems, if one exists. A link to a web site, into which I can plug a formula and get the name assigned to it, would be a very nice bonus.
physics matrix-equations
asked Jan 7 at 10:33
Omer ZakOmer Zak
1012
$endgroup$
add a comment |
$begingroup$
I am trying to solve a certain physical problem. I found a way to express the problem as one of solving the following system of equations:
$$begin{pmatrix}A_{s1}\
A_{s2}
end{pmatrix}=begin{pmatrix}f_{11}(d_{1},d_{2},d_{3},d_{4}) & f_{12}(d_{1},d_{2},d_{3},d_{4})\
f_{21}(d_{1},d_{2},d_{3},d_{4}) & f_{22}(d_{1},d_{2},d_{3},d_{4})
end{pmatrix}begin{pmatrix}A_{m1}\
A_{m2}
end{pmatrix}$$
where $A_{mj}$ and $f_{jk}$ are known; and $d_n$ are unknown but constrained to a finite volume of $ℝ^4$.
I wish to solve simultaneously for $A_{sj}$ and $d_n$. Intuition tells me that for the specific form of the $f_{jk}$ functions actually used in the problem, there is a finite or at most countably infinite number of solutions.
What I am asking in this question is for pointers to the mathematical theory which covers this kind of problems, if one exists. A link to a web site, into which I can plug a formula and get the name assigned to it, would be a very nice bonus.
physics matrix-equations
asked Jan 7 at 10:33
Omer ZakOmer Zak
1012
$endgroup$
add a comment |
$begingroup$
I am trying to solve a certain physical problem. I found a way to express the problem as one of solving the following system of equations:
$$begin{pmatrix}A_{s1}\
A_{s2}
end{pmatrix}=begin{pmatrix}f_{11}(d_{1},d_{2},d_{3},d_{4}) & f_{12}(d_{1},d_{2},d_{3},d_{4})\
f_{21}(d_{1},d_{2},d_{3},d_{4}) & f_{22}(d_{1},d_{2},d_{3},d_{4})
end{pmatrix}begin{pmatrix}A_{m1}\
A_{m2}
end{pmatrix}$$
where $A_{mj}$ and $f_{jk}$ are known; and $d_n$ are unknown but constrained to a finite volume of $ℝ^4$.
I wish to solve simultaneously for $A_{sj}$ and $d_n$. Intuition tells me that for the specific form of the $f_{jk}$ functions actually used in the problem, there is a finite or at most countably infinite number of solutions.
What I am asking in this question is for pointers to the mathematical theory which covers this kind of problems, if one exists. A link to a web site, into which I can plug a formula and get the name assigned to it, would be a very nice bonus.
physics matrix-equations
asked Jan 7 at 10:33
Omer ZakOmer Zak
1012
$endgroup$
I am trying to solve a certain physical problem. I found a way to express the problem as one of solving the following system of equations:
$$begin{pmatrix}A_{s1}\
A_{s2}
end{pmatrix}=begin{pmatrix}f_{11}(d_{1},d_{2},d_{3},d_{4}) & f_{12}(d_{1},d_{2},d_{3},d_{4})\
f_{21}(d_{1},d_{2},d_{3},d_{4}) & f_{22}(d_{1},d_{2},d_{3},d_{4})
end{pmatrix}begin{pmatrix}A_{m1}\
A_{m2}
end{pmatrix}$$
where $A_{mj}$ and $f_{jk}$ are known; and $d_n$ are unknown but constrained to a finite volume of $ℝ^4$.
I wish to solve simultaneously for $A_{sj}$ and $d_n$. Intuition tells me that for the specific form of the $f_{jk}$ functions actually used in the problem, there is a finite or at most countably infinite number of solutions.
What I am asking in this question is for pointers to the mathematical theory which covers this kind of problems, if one exists. A link to a web site, into which I can plug a formula and get the name assigned to it, would be a very nice bonus.
physics matrix-equations
physics matrix-equations
asked Jan 7 at 10:33
Omer ZakOmer Zak
1012
asked Jan 7 at 10:33
Omer ZakOmer Zak
1012
asked Jan 7 at 10:33
Omer ZakOmer Zak
1012
asked Jan 7 at 10:33
Omer ZakOmer Zak
1012
asked Jan 7 at 10:33
Omer ZakOmer Zak
1012
1012
add a comment |
add a comment |
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