Trace of tensor product

1. What is a trace of a tensor?
2. What is a trace product?
3. What is the trace of product of matrices?
4. How do you find the product of a tensor?

What is a trace of a tensor?

On a Riemannian manifold, the trace X of a tensor Xμν is defined as X=gμνXμν. In linear algebra, the trace is the sum of the diagonal elements, so a traceless matrix has the diagonal elements sum to zero.

What is a trace product?

Product traceability, is the ability to identify, track and trace elements of a product as it moves along the supply chain from raw goods to finished products. It provides numerous benefits such as the ability to investigate and troubleshoot issues related to a component or ingredient.

What is the trace of product of matrices?

Trace of a product

The trace of a square matrix which is the product of two real matrices can be rewritten as the sum of entry-wise products of their elements, i.e. as the sum of all elements of their Hadamard product.

How do you find the product of a tensor?

Definition 7.1 (Tensor product of vectors). If x, y are vectors of length M and N, respectively, their tensor product x⊗y is defined as the M ×N-matrix defined by (x ⊗ y)ij = xiyj. In other words, x ⊗ y = xyT .