Mixing
How do I calculate an x with a circle in it and a variable raised to -T?
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I am trying to design a decoupler to break a MIMO system down to a distributed SISO system for control. I am reading a paper on how to do that, but it is telling me to compute some strange stuff that I am not understanding. Please see the below computations:
How is the second equation computed? The x inside the circle usually represents the tensor product in math literature, so the dimensions of the new matrix should be the multiplication of the size of the two original matrices. Since originally, the matrices are 2x2, the resultant matrix should be 4 x 4. I assume the -T does not represent the inverse of the transpose?
exponentiation tensor-products
asked Jan 29 at 22:25
Rui NianRui Nian
1264
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add a comment |
$begingroup$
I am trying to design a decoupler to break a MIMO system down to a distributed SISO system for control. I am reading a paper on how to do that, but it is telling me to compute some strange stuff that I am not understanding. Please see the below computations:
How is the second equation computed? The x inside the circle usually represents the tensor product in math literature, so the dimensions of the new matrix should be the multiplication of the size of the two original matrices. Since originally, the matrices are 2x2, the resultant matrix should be 4 x 4. I assume the -T does not represent the inverse of the transpose?
exponentiation tensor-products
asked Jan 29 at 22:25
Rui NianRui Nian
1264
$endgroup$
add a comment |
$begingroup$
I am trying to design a decoupler to break a MIMO system down to a distributed SISO system for control. I am reading a paper on how to do that, but it is telling me to compute some strange stuff that I am not understanding. Please see the below computations:
How is the second equation computed? The x inside the circle usually represents the tensor product in math literature, so the dimensions of the new matrix should be the multiplication of the size of the two original matrices. Since originally, the matrices are 2x2, the resultant matrix should be 4 x 4. I assume the -T does not represent the inverse of the transpose?
exponentiation tensor-products
asked Jan 29 at 22:25
Rui NianRui Nian
1264
$endgroup$
I am trying to design a decoupler to break a MIMO system down to a distributed SISO system for control. I am reading a paper on how to do that, but it is telling me to compute some strange stuff that I am not understanding. Please see the below computations:
How is the second equation computed? The x inside the circle usually represents the tensor product in math literature, so the dimensions of the new matrix should be the multiplication of the size of the two original matrices. Since originally, the matrices are 2x2, the resultant matrix should be 4 x 4. I assume the -T does not represent the inverse of the transpose?
exponentiation tensor-products
exponentiation tensor-products
asked Jan 29 at 22:25
Rui NianRui Nian
1264
asked Jan 29 at 22:25
Rui NianRui Nian
1264
edited Jan 29 at 22:57
Rui Nian
asked Jan 29 at 22:25
Rui NianRui Nian
1264
asked Jan 29 at 22:25
Rui NianRui Nian
1264
asked Jan 29 at 22:25
Rui NianRui Nian
1264
1264
add a comment |
add a comment |
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Turns out the x with the circle in it did not represent a tensor product, rather, it represented an element-wise multiplication...
So it is solved by taking the transpose of the inverse of K, and then doing element-wise multiplication.
answered Jan 29 at 22:41
Rui NianRui Nian
1264
$endgroup$
add a comment |
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1 Answer
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$begingroup$
Turns out the x with the circle in it did not represent a tensor product, rather, it represented an element-wise multiplication...
So it is solved by taking the transpose of the inverse of K, and then doing element-wise multiplication.
answered Jan 29 at 22:41
Rui NianRui Nian
1264
$endgroup$
add a comment |
$begingroup$
Turns out the x with the circle in it did not represent a tensor product, rather, it represented an element-wise multiplication...
So it is solved by taking the transpose of the inverse of K, and then doing element-wise multiplication.
answered Jan 29 at 22:41
Rui NianRui Nian
1264
$endgroup$
add a comment |
$begingroup$
Turns out the x with the circle in it did not represent a tensor product, rather, it represented an element-wise multiplication...
So it is solved by taking the transpose of the inverse of K, and then doing element-wise multiplication.
answered Jan 29 at 22:41
Rui NianRui Nian
1264
$endgroup$
Turns out the x with the circle in it did not represent a tensor product, rather, it represented an element-wise multiplication...
So it is solved by taking the transpose of the inverse of K, and then doing element-wise multiplication.
answered Jan 29 at 22:41
Rui NianRui Nian
1264
answered Jan 29 at 22:41
Rui NianRui Nian
1264
answered Jan 29 at 22:41
Rui NianRui Nian
1264
answered Jan 29 at 22:41
Rui NianRui Nian
1264
1264
add a comment |
add a comment |
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