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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.