Tensor operations
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 2 days ago
Daniele Tampieri
1,5151519
asked 2 days ago
Pendelluft
62
New contributor
Pendelluft is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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 2 days ago
Daniele Tampieri
1,5151519
asked 2 days ago
Pendelluft
62
New contributor
Pendelluft is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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
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 2 days ago
Daniele Tampieri
1,5151519
asked 2 days ago
Pendelluft
62
New contributor
Pendelluft is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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 2 days ago
Daniele Tampieri
1,5151519
asked 2 days ago
Pendelluft
62
New contributor
Pendelluft is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Daniele Tampieri
1,5151519
asked 2 days ago
Pendelluft
62
New contributor
Pendelluft is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Daniele Tampieri
1,5151519
edited 2 days ago
Daniele Tampieri
1,5151519
edited 2 days ago
Daniele Tampieri
1,5151519
1,5151519
asked 2 days ago
Pendelluft
62
New contributor
Pendelluft is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Pendelluft
62
asked 2 days ago
Pendelluft
62
62
New contributor
Pendelluft is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Pendelluft is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Pendelluft is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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
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
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
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
2 days ago
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Pendelluft is a new contributor. Be nice, and check out our Code of Conduct.
Pendelluft is a new contributor. Be nice, and check out our Code of Conduct.
Pendelluft is a new contributor. Be nice, and check out our Code of Conduct.
Pendelluft is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2999245%2ftensor-operations%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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
2 days ago