Mixing
What are the branches of mathematics that deal with finding common transformations between matrices
$begingroup$
First I will apologize early for my lack of mathematical knowledge. I am sorry.
If I want to find a or all common transformation matrices X or even functions if that is possible such that
$$
begin{pmatrix}
a_x & b_x & c_x \
b_x & c_x & b_x \
a_x & a_x & c_x \
end{pmatrix} cdot X = begin{pmatrix}
b_x & c_x & a_x \
b_x & a_x & b_x \
a_x & c_x & c_x \
end{pmatrix} = K
$$
$$ K cdot X =
begin{pmatrix}
b_x & a_x & b_x \
c_x & a_x & c_x \
a_x & c_x & b_x \
end{pmatrix}
$$
Where the subscript $$x = 1lor2lor3 $$
such that all $$a_xlor b_xlor c_x$$ require to be of the form $$a_1,a_2,a_3$$ $$b_1,b_2,b_3$$ $$c_1,c_2,c_3$$
such that per matrix there are no two $$a_1$$ and such that $$a_1$$ can not turn into either $$a_2 lor a_3$$ and the same applies to $$b_x$$ and also $$c_x$$
What branches of mathematics would deal with such problems?
Also again apologies for my likely incorrect use logic symbol or to signify 'or' in general and my formatting.
linear-algebra matrices matrix-equations
asked Jan 25 at 20:56
John SchneiderJohn Schneider
1
$endgroup$
add a comment |
$begingroup$
First I will apologize early for my lack of mathematical knowledge. I am sorry.
If I want to find a or all common transformation matrices X or even functions if that is possible such that
$$
begin{pmatrix}
a_x & b_x & c_x \
b_x & c_x & b_x \
a_x & a_x & c_x \
end{pmatrix} cdot X = begin{pmatrix}
b_x & c_x & a_x \
b_x & a_x & b_x \
a_x & c_x & c_x \
end{pmatrix} = K
$$
$$ K cdot X =
begin{pmatrix}
b_x & a_x & b_x \
c_x & a_x & c_x \
a_x & c_x & b_x \
end{pmatrix}
$$
Where the subscript $$x = 1lor2lor3 $$
such that all $$a_xlor b_xlor c_x$$ require to be of the form $$a_1,a_2,a_3$$ $$b_1,b_2,b_3$$ $$c_1,c_2,c_3$$
such that per matrix there are no two $$a_1$$ and such that $$a_1$$ can not turn into either $$a_2 lor a_3$$ and the same applies to $$b_x$$ and also $$c_x$$
What branches of mathematics would deal with such problems?
Also again apologies for my likely incorrect use logic symbol or to signify 'or' in general and my formatting.
linear-algebra matrices matrix-equations
asked Jan 25 at 20:56
John SchneiderJohn Schneider
1
$endgroup$
$begingroup$
Linear algebra. Possibly group theory, if you want to understand the structure of the transformations.
$endgroup$
– David G. Stork
Jan 25 at 21:48
$begingroup$
I wouldn't be surprised if there were no more sophisticated techniques than just brute forcing the problem with elementary linear algebra.
$endgroup$
– Jack M
Jan 25 at 22:26
$begingroup$
It's not clear what your conditions mean though. What does it mean for $a_1$ to "turn into" $a_2$ or $a_3$?
$endgroup$
– Jack M
Jan 25 at 22:27
$begingroup$
@JackM I was thinking of linear algebra but wasn't sure if that was enough for doing this without brute forcing if there are no more sophisticated techniques then there is no choice I suppose. Also apologies for not being clear, $a_1$ turning into $a_2$ or $a_3$ simply was to clarify that the position of any of the variables is unique once they are set initially, so that the goal is not simply to get any $a_x$ in that position but which ever required $a_n$ that was set initially.
$endgroup$
– John Schneider
Jan 26 at 11:59
$begingroup$
@DavidG.Stork It seems group theory and linear algebra are indeed very much required to what I was hoping for, thank you.
$endgroup$
– John Schneider
Jan 26 at 12:03
add a comment |
$begingroup$
First I will apologize early for my lack of mathematical knowledge. I am sorry.
If I want to find a or all common transformation matrices X or even functions if that is possible such that
$$
begin{pmatrix}
a_x & b_x & c_x \
b_x & c_x & b_x \
a_x & a_x & c_x \
end{pmatrix} cdot X = begin{pmatrix}
b_x & c_x & a_x \
b_x & a_x & b_x \
a_x & c_x & c_x \
end{pmatrix} = K
$$
$$ K cdot X =
begin{pmatrix}
b_x & a_x & b_x \
c_x & a_x & c_x \
a_x & c_x & b_x \
end{pmatrix}
$$
Where the subscript $$x = 1lor2lor3 $$
such that all $$a_xlor b_xlor c_x$$ require to be of the form $$a_1,a_2,a_3$$ $$b_1,b_2,b_3$$ $$c_1,c_2,c_3$$
such that per matrix there are no two $$a_1$$ and such that $$a_1$$ can not turn into either $$a_2 lor a_3$$ and the same applies to $$b_x$$ and also $$c_x$$
What branches of mathematics would deal with such problems?
Also again apologies for my likely incorrect use logic symbol or to signify 'or' in general and my formatting.
linear-algebra matrices matrix-equations
asked Jan 25 at 20:56
John SchneiderJohn Schneider
1
$endgroup$
First I will apologize early for my lack of mathematical knowledge. I am sorry.
If I want to find a or all common transformation matrices X or even functions if that is possible such that
$$
begin{pmatrix}
a_x & b_x & c_x \
b_x & c_x & b_x \
a_x & a_x & c_x \
end{pmatrix} cdot X = begin{pmatrix}
b_x & c_x & a_x \
b_x & a_x & b_x \
a_x & c_x & c_x \
end{pmatrix} = K
$$
$$ K cdot X =
begin{pmatrix}
b_x & a_x & b_x \
c_x & a_x & c_x \
a_x & c_x & b_x \
end{pmatrix}
$$
Where the subscript $$x = 1lor2lor3 $$
such that all $$a_xlor b_xlor c_x$$ require to be of the form $$a_1,a_2,a_3$$ $$b_1,b_2,b_3$$ $$c_1,c_2,c_3$$
such that per matrix there are no two $$a_1$$ and such that $$a_1$$ can not turn into either $$a_2 lor a_3$$ and the same applies to $$b_x$$ and also $$c_x$$
What branches of mathematics would deal with such problems?
Also again apologies for my likely incorrect use logic symbol or to signify 'or' in general and my formatting.
linear-algebra matrices matrix-equations
linear-algebra matrices matrix-equations
asked Jan 25 at 20:56
John SchneiderJohn Schneider
1
asked Jan 25 at 20:56
John SchneiderJohn Schneider
1
asked Jan 25 at 20:56
John SchneiderJohn Schneider
1
asked Jan 25 at 20:56
John SchneiderJohn Schneider
1
asked Jan 25 at 20:56
John SchneiderJohn Schneider
1
1
$begingroup$
Linear algebra. Possibly group theory, if you want to understand the structure of the transformations.
$endgroup$
– David G. Stork
Jan 25 at 21:48
$begingroup$
I wouldn't be surprised if there were no more sophisticated techniques than just brute forcing the problem with elementary linear algebra.
$endgroup$
– Jack M
Jan 25 at 22:26
$begingroup$
It's not clear what your conditions mean though. What does it mean for $a_1$ to "turn into" $a_2$ or $a_3$?
$endgroup$
– Jack M
Jan 25 at 22:27
$begingroup$
@JackM I was thinking of linear algebra but wasn't sure if that was enough for doing this without brute forcing if there are no more sophisticated techniques then there is no choice I suppose. Also apologies for not being clear, $a_1$ turning into $a_2$ or $a_3$ simply was to clarify that the position of any of the variables is unique once they are set initially, so that the goal is not simply to get any $a_x$ in that position but which ever required $a_n$ that was set initially.
$endgroup$
– John Schneider
Jan 26 at 11:59
$begingroup$
@DavidG.Stork It seems group theory and linear algebra are indeed very much required to what I was hoping for, thank you.
$endgroup$
– John Schneider
Jan 26 at 12:03
add a comment |
$begingroup$
Linear algebra. Possibly group theory, if you want to understand the structure of the transformations.
$endgroup$
– David G. Stork
Jan 25 at 21:48
$begingroup$
I wouldn't be surprised if there were no more sophisticated techniques than just brute forcing the problem with elementary linear algebra.
$endgroup$
– Jack M
Jan 25 at 22:26
$begingroup$
It's not clear what your conditions mean though. What does it mean for $a_1$ to "turn into" $a_2$ or $a_3$?
$endgroup$
– Jack M
Jan 25 at 22:27
$begingroup$
@JackM I was thinking of linear algebra but wasn't sure if that was enough for doing this without brute forcing if there are no more sophisticated techniques then there is no choice I suppose. Also apologies for not being clear, $a_1$ turning into $a_2$ or $a_3$ simply was to clarify that the position of any of the variables is unique once they are set initially, so that the goal is not simply to get any $a_x$ in that position but which ever required $a_n$ that was set initially.
$endgroup$
– John Schneider
Jan 26 at 11:59
$begingroup$
@DavidG.Stork It seems group theory and linear algebra are indeed very much required to what I was hoping for, thank you.
$endgroup$
– John Schneider
Jan 26 at 12:03
$begingroup$
Linear algebra. Possibly group theory, if you want to understand the structure of the transformations.
$endgroup$
– David G. Stork
Jan 25 at 21:48
$begingroup$
Linear algebra. Possibly group theory, if you want to understand the structure of the transformations.
$endgroup$
– David G. Stork
Jan 25 at 21:48
$begingroup$
I wouldn't be surprised if there were no more sophisticated techniques than just brute forcing the problem with elementary linear algebra.
$endgroup$
– Jack M
Jan 25 at 22:26
$begingroup$
I wouldn't be surprised if there were no more sophisticated techniques than just brute forcing the problem with elementary linear algebra.
$endgroup$
– Jack M
Jan 25 at 22:26
$begingroup$
It's not clear what your conditions mean though. What does it mean for $a_1$ to "turn into" $a_2$ or $a_3$?
$endgroup$
– Jack M
Jan 25 at 22:27
$begingroup$
It's not clear what your conditions mean though. What does it mean for $a_1$ to "turn into" $a_2$ or $a_3$?
$endgroup$
– Jack M
Jan 25 at 22:27
$begingroup$
@JackM I was thinking of linear algebra but wasn't sure if that was enough for doing this without brute forcing if there are no more sophisticated techniques then there is no choice I suppose. Also apologies for not being clear, $a_1$ turning into $a_2$ or $a_3$ simply was to clarify that the position of any of the variables is unique once they are set initially, so that the goal is not simply to get any $a_x$ in that position but which ever required $a_n$ that was set initially.
$endgroup$
– John Schneider
Jan 26 at 11:59
$begingroup$
@JackM I was thinking of linear algebra but wasn't sure if that was enough for doing this without brute forcing if there are no more sophisticated techniques then there is no choice I suppose. Also apologies for not being clear, $a_1$ turning into $a_2$ or $a_3$ simply was to clarify that the position of any of the variables is unique once they are set initially, so that the goal is not simply to get any $a_x$ in that position but which ever required $a_n$ that was set initially.
$endgroup$
– John Schneider
Jan 26 at 11:59
$begingroup$
@DavidG.Stork It seems group theory and linear algebra are indeed very much required to what I was hoping for, thank you.
$endgroup$
– John Schneider
Jan 26 at 12:03
$begingroup$
@DavidG.Stork It seems group theory and linear algebra are indeed very much required to what I was hoping for, thank you.
$endgroup$
– John Schneider
Jan 26 at 12:03
add a comment |
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$begingroup$
Linear algebra. Possibly group theory, if you want to understand the structure of the transformations.
$endgroup$
– David G. Stork
Jan 25 at 21:48
$begingroup$
I wouldn't be surprised if there were no more sophisticated techniques than just brute forcing the problem with elementary linear algebra.
$endgroup$
– Jack M
Jan 25 at 22:26
$begingroup$
It's not clear what your conditions mean though. What does it mean for $a_1$ to "turn into" $a_2$ or $a_3$?
$endgroup$
– Jack M
Jan 25 at 22:27
$begingroup$
@JackM I was thinking of linear algebra but wasn't sure if that was enough for doing this without brute forcing if there are no more sophisticated techniques then there is no choice I suppose. Also apologies for not being clear, $a_1$ turning into $a_2$ or $a_3$ simply was to clarify that the position of any of the variables is unique once they are set initially, so that the goal is not simply to get any $a_x$ in that position but which ever required $a_n$ that was set initially.
$endgroup$
– John Schneider
Jan 26 at 11:59
$begingroup$
@DavidG.Stork It seems group theory and linear algebra are indeed very much required to what I was hoping for, thank you.
$endgroup$
– John Schneider
Jan 26 at 12:03