A tensor of rank 1 is required to represent the electric field surrounding a point charge in space or the gravitational field of a massive object. A tensor of rank 2 is necessary to represent a magnetic …

May 25, 2016 · The bottom line is that as long as the tensor expression makes sense and the intention is clear, such repetitions should be allowed with no need in our view to take special precaution like …

Equation (1-49) is valid for all components of the extra stress tensor in any flow of a Newtonian fluid. All low molar mass liquids are Newtonian (such as water, benzene, etc.)

Final Draft: March 25, 2025. Notice: This material will be published by Cambridge University Press as Tensor Decompositions for Data Science by Grey Ballard and Tamara G. Kolda. This pre-publication …

This produces a new tensor with the same index structure as the previous, but with lower index in the position of the contracted upper index. This operation is as lowering an index.

Vectors are simple and well-known examples of tensors, but there is much more to tensor theory than vectors. The second chapter discusses tensor fields and curvilinear coordinates. It is this chapter …

Figure 4.2. The central idea is to reduce the dimensions of the tensor A and matrix B with sampling to get C and R, and perform an n-mode matrix product with C and R using the classica