Data type in tensors [closed]
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I know that there are kinds of tensors: scalars, vectors and matrixes. I know they contain data in form of numbers, but what bugs me is what kind of data is represented in a tensor and what do we do to get that data? Its not just a collection some random numbers, but calculated ones are put in there. Out of what do we get those numbers?
Sorry if this may sound stupid...
tensor-products tensors
asked Aug 27 at 15:15
Aleksandar Kostovic
82
closed as off-topic by Hans Lundmark, Nick, Vladhagen, Xander Henderson, Shailesh Aug 28 at 0:10
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Nick, Shailesh
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I know that there are kinds of tensors: scalars, vectors and matrixes. I know they contain data in form of numbers, but what bugs me is what kind of data is represented in a tensor and what do we do to get that data? Its not just a collection some random numbers, but calculated ones are put in there. Out of what do we get those numbers?
Sorry if this may sound stupid...
tensor-products tensors
asked Aug 27 at 15:15
Aleksandar Kostovic
82
closed as off-topic by Hans Lundmark, Nick, Vladhagen, Xander Henderson, Shailesh Aug 28 at 0:10
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Nick, Shailesh
Well, out of what do we get the scalar numbers (0-tensor), the numbers in a vector (1-tensor) and the numbers in a matrix (2-tensor)?
– md2perpe
Aug 27 at 15:29
@md2perpe IDK. Could you please explain?
– Aleksandar Kostovic
Aug 27 at 16:49
Maybe this can help you, it helped me back then
– Giuseppe Negro
Aug 27 at 16:56
In physics the numbers often come from measurements.
– md2perpe
Aug 27 at 20:10
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I know that there are kinds of tensors: scalars, vectors and matrixes. I know they contain data in form of numbers, but what bugs me is what kind of data is represented in a tensor and what do we do to get that data? Its not just a collection some random numbers, but calculated ones are put in there. Out of what do we get those numbers?
Sorry if this may sound stupid...
tensor-products tensors
asked Aug 27 at 15:15
Aleksandar Kostovic
82
I know that there are kinds of tensors: scalars, vectors and matrixes. I know they contain data in form of numbers, but what bugs me is what kind of data is represented in a tensor and what do we do to get that data? Its not just a collection some random numbers, but calculated ones are put in there. Out of what do we get those numbers?
Sorry if this may sound stupid...
tensor-products tensors
asked Aug 27 at 15:15
Aleksandar Kostovic
82
asked Aug 27 at 15:15
Aleksandar Kostovic
82
asked Aug 27 at 15:15
Aleksandar Kostovic
82
asked Aug 27 at 15:15
Aleksandar Kostovic
82
82
closed as off-topic by Hans Lundmark, Nick, Vladhagen, Xander Henderson, Shailesh Aug 28 at 0:10
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Nick, Shailesh
closed as off-topic by Hans Lundmark, Nick, Vladhagen, Xander Henderson, Shailesh Aug 28 at 0:10
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Nick, Shailesh
Well, out of what do we get the scalar numbers (0-tensor), the numbers in a vector (1-tensor) and the numbers in a matrix (2-tensor)?
– md2perpe
Aug 27 at 15:29
@md2perpe IDK. Could you please explain?
– Aleksandar Kostovic
Aug 27 at 16:49
Maybe this can help you, it helped me back then
– Giuseppe Negro
Aug 27 at 16:56
In physics the numbers often come from measurements.
– md2perpe
Aug 27 at 20:10
add a comment |Â
Well, out of what do we get the scalar numbers (0-tensor), the numbers in a vector (1-tensor) and the numbers in a matrix (2-tensor)?
– md2perpe
Aug 27 at 15:29
@md2perpe IDK. Could you please explain?
– Aleksandar Kostovic
Aug 27 at 16:49
Maybe this can help you, it helped me back then
– Giuseppe Negro
Aug 27 at 16:56
In physics the numbers often come from measurements.
– md2perpe
Aug 27 at 20:10
Well, out of what do we get the scalar numbers (0-tensor), the numbers in a vector (1-tensor) and the numbers in a matrix (2-tensor)?
– md2perpe
Aug 27 at 15:29
Well, out of what do we get the scalar numbers (0-tensor), the numbers in a vector (1-tensor) and the numbers in a matrix (2-tensor)?
– md2perpe
Aug 27 at 15:29
@md2perpe IDK. Could you please explain?
– Aleksandar Kostovic
Aug 27 at 16:49
@md2perpe IDK. Could you please explain?
– Aleksandar Kostovic
Aug 27 at 16:49
Maybe this can help you, it helped me back then
– Giuseppe Negro
Aug 27 at 16:56
Maybe this can help you, it helped me back then
– Giuseppe Negro
Aug 27 at 16:56
In physics the numbers often come from measurements.
– md2perpe
Aug 27 at 20:10
In physics the numbers often come from measurements.
– md2perpe
Aug 27 at 20:10
add a comment |Â
1 Answer
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In a geometrical perspective a 0-tensor is simply a number (a real scalar for example) and a 0-tensor field in a region $Omega$ is a simply a (real) scalar-field $OmegatoBbb R$.
A rank one tensor is an operator derivative $X$ which alows to speak of how a scalar field varies in direction of the $X$, being $X$ a linear combination $X=X^spartial_s$ ot the basic derivatives $partial_s=fracpartialpartial x^s$.
Since the components are function of the coordinates we should be speaking of rank one tensor fields
The metric tensor is a rank two tensor which generalize the analogous of an interior product on $Bbb R^2$ and $Bbb R^3$ and its uses there.
It is defined as the bilinear map $g=g^stpartial_sotimespartial_t$ and the coefficients $g_st=partial_scdotpartial_t$.
In a flat euclidean space we have $g_st=delta_st$, but in a space with curvilinear coordinates we would have $g_smug^mu t=delta_s^t$.
This mechanism allows to model the geometrical distortions living on where the coordinates are employed.
With the aid of the low and raise indexation technique one can construct associated tensors
for example
$$A_i^jk=g_isA^sjk.$$
and with those one reduces the amount of data to manipulate any rank tensors.
answered Aug 27 at 16:52
janmarqz
6,08441629
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
In a geometrical perspective a 0-tensor is simply a number (a real scalar for example) and a 0-tensor field in a region $Omega$ is a simply a (real) scalar-field $OmegatoBbb R$.
A rank one tensor is an operator derivative $X$ which alows to speak of how a scalar field varies in direction of the $X$, being $X$ a linear combination $X=X^spartial_s$ ot the basic derivatives $partial_s=fracpartialpartial x^s$.
Since the components are function of the coordinates we should be speaking of rank one tensor fields
The metric tensor is a rank two tensor which generalize the analogous of an interior product on $Bbb R^2$ and $Bbb R^3$ and its uses there.
It is defined as the bilinear map $g=g^stpartial_sotimespartial_t$ and the coefficients $g_st=partial_scdotpartial_t$.
In a flat euclidean space we have $g_st=delta_st$, but in a space with curvilinear coordinates we would have $g_smug^mu t=delta_s^t$.
This mechanism allows to model the geometrical distortions living on where the coordinates are employed.
With the aid of the low and raise indexation technique one can construct associated tensors
for example
$$A_i^jk=g_isA^sjk.$$
and with those one reduces the amount of data to manipulate any rank tensors.
answered Aug 27 at 16:52
janmarqz
6,08441629
add a comment |Â
up vote
0
down vote
accepted
In a geometrical perspective a 0-tensor is simply a number (a real scalar for example) and a 0-tensor field in a region $Omega$ is a simply a (real) scalar-field $OmegatoBbb R$.
A rank one tensor is an operator derivative $X$ which alows to speak of how a scalar field varies in direction of the $X$, being $X$ a linear combination $X=X^spartial_s$ ot the basic derivatives $partial_s=fracpartialpartial x^s$.
Since the components are function of the coordinates we should be speaking of rank one tensor fields
The metric tensor is a rank two tensor which generalize the analogous of an interior product on $Bbb R^2$ and $Bbb R^3$ and its uses there.
It is defined as the bilinear map $g=g^stpartial_sotimespartial_t$ and the coefficients $g_st=partial_scdotpartial_t$.
In a flat euclidean space we have $g_st=delta_st$, but in a space with curvilinear coordinates we would have $g_smug^mu t=delta_s^t$.
This mechanism allows to model the geometrical distortions living on where the coordinates are employed.
With the aid of the low and raise indexation technique one can construct associated tensors
for example
$$A_i^jk=g_isA^sjk.$$
and with those one reduces the amount of data to manipulate any rank tensors.
answered Aug 27 at 16:52
janmarqz
6,08441629
add a comment |Â
up vote
0
down vote
accepted
up vote
0
down vote
accepted
In a geometrical perspective a 0-tensor is simply a number (a real scalar for example) and a 0-tensor field in a region $Omega$ is a simply a (real) scalar-field $OmegatoBbb R$.
A rank one tensor is an operator derivative $X$ which alows to speak of how a scalar field varies in direction of the $X$, being $X$ a linear combination $X=X^spartial_s$ ot the basic derivatives $partial_s=fracpartialpartial x^s$.
Since the components are function of the coordinates we should be speaking of rank one tensor fields
The metric tensor is a rank two tensor which generalize the analogous of an interior product on $Bbb R^2$ and $Bbb R^3$ and its uses there.
It is defined as the bilinear map $g=g^stpartial_sotimespartial_t$ and the coefficients $g_st=partial_scdotpartial_t$.
In a flat euclidean space we have $g_st=delta_st$, but in a space with curvilinear coordinates we would have $g_smug^mu t=delta_s^t$.
This mechanism allows to model the geometrical distortions living on where the coordinates are employed.
With the aid of the low and raise indexation technique one can construct associated tensors
for example
$$A_i^jk=g_isA^sjk.$$
and with those one reduces the amount of data to manipulate any rank tensors.
answered Aug 27 at 16:52
janmarqz
6,08441629
In a geometrical perspective a 0-tensor is simply a number (a real scalar for example) and a 0-tensor field in a region $Omega$ is a simply a (real) scalar-field $OmegatoBbb R$.
A rank one tensor is an operator derivative $X$ which alows to speak of how a scalar field varies in direction of the $X$, being $X$ a linear combination $X=X^spartial_s$ ot the basic derivatives $partial_s=fracpartialpartial x^s$.
Since the components are function of the coordinates we should be speaking of rank one tensor fields
The metric tensor is a rank two tensor which generalize the analogous of an interior product on $Bbb R^2$ and $Bbb R^3$ and its uses there.
It is defined as the bilinear map $g=g^stpartial_sotimespartial_t$ and the coefficients $g_st=partial_scdotpartial_t$.
In a flat euclidean space we have $g_st=delta_st$, but in a space with curvilinear coordinates we would have $g_smug^mu t=delta_s^t$.
This mechanism allows to model the geometrical distortions living on where the coordinates are employed.
With the aid of the low and raise indexation technique one can construct associated tensors
for example
$$A_i^jk=g_isA^sjk.$$
and with those one reduces the amount of data to manipulate any rank tensors.
answered Aug 27 at 16:52
janmarqz
6,08441629
answered Aug 27 at 16:52
janmarqz
6,08441629
answered Aug 27 at 16:52
janmarqz
6,08441629
answered Aug 27 at 16:52
janmarqz
6,08441629
6,08441629
add a comment |Â
add a comment |Â
Well, out of what do we get the scalar numbers (0-tensor), the numbers in a vector (1-tensor) and the numbers in a matrix (2-tensor)?
– md2perpe
Aug 27 at 15:29
@md2perpe IDK. Could you please explain?
– Aleksandar Kostovic
Aug 27 at 16:49
Maybe this can help you, it helped me back then
– Giuseppe Negro
Aug 27 at 16:56
In physics the numbers often come from measurements.
– md2perpe
Aug 27 at 20:10