Tensor help!

[ComradeRed]

Does anyone understand tensors? I am trying to understand the distortion of spacetime as Einstein theorized about, but I do not understand how to interpret tensors. Is it a number of row and column vectors combined?

[Starboy]

Do you know any linear algebra?

Starboy

[ComradeRed]

Yes, of course.

[Starboy]

Good. A scalar is a 1-tuple and a tensor of order 0. A vector is an n-tuple or a tensor of order 1. A matrix is an nxm tuple and is a tensor of order 2. Such a tensor is usually used to transform a vector in one vector space to another vector space (coordinate tranformations). However a matrix may also be used to describe the stress of a space in a particular coordinate system. There will then be a higher order tensor that can be used to transform that stress matrix or tensor into another coordinate space. And of course one can concoct physical concepts that require even higher order collections of nxmxp-tuples that will again need to be transformed from one space to another.

Starboy

[gallo]

Quote by: Starboy Good. A scalar is a 1-tuple and a tensor of order 0. A vector is an n-tuple or a tensor of order 1. A matrix is an nxm tuple and is a tensor of order 2. Such a tensor is usually used to transform a vector in one vector space to another vector space (coordinate tranformations). However a matrix may also be used to describe the stress of a space in a particular coordinate system. There will then be a higher order tensor that can be used to transform that stress matrix or tensor into another coordinate space. And of course one can concoct physical concepts that require even higher order collections of nxmxp-tuples that will again need to be transformed from one space to another. Starboy

Well that blew my mind. I have no idea what you just said. However, both of my sons do. One is a graduate nuclear engineer and the other is a BS in math. Both took linear algebra and both agreed that is sucked. They actually tried to explain tensors to me once. They weren't all that successful. All I got was that a tensor is a vector matrix and an operation performed on any one vector is also performed on the entire matrix. I'm not all that secure in that understanding. I do grasp multidimensional arrays since I programmed databases with them for over 20 years. But I think any analogy between the two would be a stretch.

The whole subject came up when a creationist brought up the subject as some sort of "proof" of creationism. My elder son responded with some actual math and the creationist vanished. I didn't understand any of it.

[Prometheus]

I didn't know we had mathematicians on this forum...

In high school I was pretty hot stuff with my calculus and number theory... but I seem to have fallen behind the curve in mathamatics at the university level. The biology has taken over my life, although multivariable calculus cames next semester (kill me now).

[rcne]

Quote by: Starboy Good. A scalar is a 1-tuple and a tensor of order 0. A vector is an n-tuple or a tensor of order 1. A matrix is an nxm tuple and is a tensor of order 2. Such a tensor is usually used to transform a vector in one vector space to another vector space (coordinate tranformations). However a matrix may also be used to describe the stress of a space in a particular coordinate system. There will then be a higher order tensor that can be used to transform that stress matrix or tensor into another coordinate space. And of course one can concoct physical concepts that require even higher order collections of nxmxp-tuples that will again need to be transformed from one space to another. Starboy

Good stuff Starboy, a quick and concise description. At least at my understanding level.

Did you get that in Time - ComradRed. (pun intended)

[Sonart]

Math!!! Eeeek!!!



.

[tman_ndsu08]

Quote by: Prometheus I didn't know we had mathematicians on this forum... In high school I was pretty hot stuff with my calculus and number theory... but I seem to have fallen behind the curve in mathamatics at the university level. The biology has taken over my life, although multivariable calculus cames next semester (kill me now).

Well, mathematicians have been hard at work, recently, creating tensor math to help study problems in physics and engineering.

Oh wait, that was back in the late 1800's.

[tman_ndsu08]

Quote by: ComradeRed Does anyone understand tensors?

No...but I did sleep at a Holiday Inn Express last night!

http://en.wikipedia.org/wiki/Tensor

[Prometheus]

Quote by: tman_ndsu08 Well, mathematicians have been hard at work, recently, creating tensor math to help study problems in physics and engineering. Oh wait, that was back in the late 1800's.

Are you mocking me for not understanding this crap? You don't even understand it yourself. Ass.

[rcne]

Few people on this planet understand 'fully' the concepts of Tensor maths. I've read a fair deal about it/them and think I understand 'some' of it.

Few would even claim to understand it - and most of those - well......

Anyhow, back to the original post, there are a few good sites on the net that present tensor math at differing levels of difficulty..

Now ....if I could only get the concept of entanglement condensed down to a couple of paragraphs.

[Starboy]

Ya gotta love those mathematicians. The "pure" mathematicians deal in complete abstraction. They don't care what a tensor represents nor do they care if it can be used in the physical world at all. Some of them get bummed out when some dang physcist finds a use for their mathematics. To them it is a mental game of pure abstraction to play with.

Starboy

[ComradeRed]

Good. A scalar is a 1-tuple and a tensor of order 0. A vector is an n-tuple or a tensor of order 1. A matrix is an nxm tuple and is a tensor of order 2. Such a tensor is usually used to transform a vector in one vector space to another vector space (coordinate tranformations). However a matrix may also be used to describe the stress of a space in a particular coordinate system. There will then be a higher order tensor that can be used to transform that stress matrix or tensor into another coordinate space. And of course one can concoct physical concepts that require even higher order collections of nxmxp-tuples that will again need to be transformed from one space to another.

Right, so how exactly (when given a vector or tensor) would one transform its coordinates? Or would this fall into tensor calculus?