Tensor operations
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I'm trying to do some scientific programming, but I have limited math experience. My supervisor has given me the following equation I need to solve for $d$:
$$
Y = Xe^{-bcdot d}.
$$
where
$X$ and $Y$ are $96 times 96$ matrices,- and $b$ and $d$ are $3times 3$ matrices (the '$cdot$' sing above signifies dot product).
I'm not even sure how I would go about trying to solve for $d$. It doesn't seem to make sense to rearrange the equation above to
$$
d = mathrm{inv}(b) ln(X/Y),
$$
since (1) I'm not sure how dot product works with tensors (do I need to learn dyadic algebra to do this???), but I didn't think you could just do $mathrm{inv}(b)(bcdot d)$. And how are you supposed to end up with a $3times 3$ matrix if you're multiplying a $3times 3$ matrix by a $96times 96$ one?
If anyone could please give suggest some resources or give me some direction, I would be sincerely appreciative, and thank you for your time.
matrix-equations tensors matrix-calculus
edited Nov 15 at 6:11
Daniele Tampieri
1,5451619
asked Nov 15 at 5:04
Pendelluft
62
add a comment |
up vote
1
down vote
favorite
I'm trying to do some scientific programming, but I have limited math experience. My supervisor has given me the following equation I need to solve for $d$:
$$
Y = Xe^{-bcdot d}.
$$
where
$X$ and $Y$ are $96 times 96$ matrices,- and $b$ and $d$ are $3times 3$ matrices (the '$cdot$' sing above signifies dot product).
I'm not even sure how I would go about trying to solve for $d$. It doesn't seem to make sense to rearrange the equation above to
$$
d = mathrm{inv}(b) ln(X/Y),
$$
since (1) I'm not sure how dot product works with tensors (do I need to learn dyadic algebra to do this???), but I didn't think you could just do $mathrm{inv}(b)(bcdot d)$. And how are you supposed to end up with a $3times 3$ matrix if you're multiplying a $3times 3$ matrix by a $96times 96$ one?
If anyone could please give suggest some resources or give me some direction, I would be sincerely appreciative, and thank you for your time.
matrix-equations tensors matrix-calculus
edited Nov 15 at 6:11
Daniele Tampieri
1,5451619
asked Nov 15 at 5:04
Pendelluft
62
Perhaps the notation $(bcdot d)$ is meant to denote the scalar product of the two matrices, i.e. $$bcdot d = sum_{ij} b_{ij}d_{ij}$$
– greg
Nov 15 at 17:40
That is exactly what it was :) Thank you so much.
– Pendelluft
2 days ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I'm trying to do some scientific programming, but I have limited math experience. My supervisor has given me the following equation I need to solve for $d$:
$$
Y = Xe^{-bcdot d}.
$$
where
$X$ and $Y$ are $96 times 96$ matrices,- and $b$ and $d$ are $3times 3$ matrices (the '$cdot$' sing above signifies dot product).
I'm not even sure how I would go about trying to solve for $d$. It doesn't seem to make sense to rearrange the equation above to
$$
d = mathrm{inv}(b) ln(X/Y),
$$
since (1) I'm not sure how dot product works with tensors (do I need to learn dyadic algebra to do this???), but I didn't think you could just do $mathrm{inv}(b)(bcdot d)$. And how are you supposed to end up with a $3times 3$ matrix if you're multiplying a $3times 3$ matrix by a $96times 96$ one?
If anyone could please give suggest some resources or give me some direction, I would be sincerely appreciative, and thank you for your time.
matrix-equations tensors matrix-calculus
edited Nov 15 at 6:11
Daniele Tampieri
1,5451619
asked Nov 15 at 5:04
Pendelluft
62
I'm trying to do some scientific programming, but I have limited math experience. My supervisor has given me the following equation I need to solve for $d$:
$$
Y = Xe^{-bcdot d}.
$$
where
$X$ and $Y$ are $96 times 96$ matrices,- and $b$ and $d$ are $3times 3$ matrices (the '$cdot$' sing above signifies dot product).
I'm not even sure how I would go about trying to solve for $d$. It doesn't seem to make sense to rearrange the equation above to
$$
d = mathrm{inv}(b) ln(X/Y),
$$
since (1) I'm not sure how dot product works with tensors (do I need to learn dyadic algebra to do this???), but I didn't think you could just do $mathrm{inv}(b)(bcdot d)$. And how are you supposed to end up with a $3times 3$ matrix if you're multiplying a $3times 3$ matrix by a $96times 96$ one?
If anyone could please give suggest some resources or give me some direction, I would be sincerely appreciative, and thank you for your time.
matrix-equations tensors matrix-calculus
matrix-equations tensors matrix-calculus
edited Nov 15 at 6:11
Daniele Tampieri
1,5451619
asked Nov 15 at 5:04
Pendelluft
62
edited Nov 15 at 6:11
Daniele Tampieri
1,5451619
asked Nov 15 at 5:04
Pendelluft
62
edited Nov 15 at 6:11
Daniele Tampieri
1,5451619
edited Nov 15 at 6:11
Daniele Tampieri
1,5451619
edited Nov 15 at 6:11
Daniele Tampieri
1,5451619
1,5451619
asked Nov 15 at 5:04
Pendelluft
62
asked Nov 15 at 5:04
Pendelluft
62
asked Nov 15 at 5:04
Pendelluft
62
62
Perhaps the notation $(bcdot d)$ is meant to denote the scalar product of the two matrices, i.e. $$bcdot d = sum_{ij} b_{ij}d_{ij}$$
– greg
Nov 15 at 17:40
That is exactly what it was :) Thank you so much.
– Pendelluft
2 days ago
add a comment |
Perhaps the notation $(bcdot d)$ is meant to denote the scalar product of the two matrices, i.e. $$bcdot d = sum_{ij} b_{ij}d_{ij}$$
– greg
Nov 15 at 17:40
That is exactly what it was :) Thank you so much.
– Pendelluft
2 days ago
Perhaps the notation $(bcdot d)$ is meant to denote the scalar product of the two matrices, i.e. $$bcdot d = sum_{ij} b_{ij}d_{ij}$$
– greg
Nov 15 at 17:40
Perhaps the notation $(bcdot d)$ is meant to denote the scalar product of the two matrices, i.e. $$bcdot d = sum_{ij} b_{ij}d_{ij}$$
– greg
Nov 15 at 17:40
That is exactly what it was :) Thank you so much.
– Pendelluft
2 days ago
That is exactly what it was :) Thank you so much.
– Pendelluft
2 days ago
add a comment |
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Perhaps the notation $(bcdot d)$ is meant to denote the scalar product of the two matrices, i.e. $$bcdot d = sum_{ij} b_{ij}d_{ij}$$
– greg
Nov 15 at 17:40
That is exactly what it was :) Thank you so much.
– Pendelluft
2 days ago