Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Richard777 on 12/01/2020 13:39:15

Title: Can a tensor be represented as the average of vector triple products?
Post by: Richard777 on 12/01/2020 13:39:15
Generally a tensor may be represented as a product of vectors.

A “reducing tensor” may be represented as the average of vector triple products. A reducing tensor will also “reduce” to an average of scalar products.

Acceleration may be represented as a vector. A field (gravitational, electric, or magnetic) may be represented using “reducing tensors” of acceleration.

An “equivalent EFE” may be written as reducing tensors. The equivalent EFE will then reduce to scalar products of acceleration. Suitable definitions of acceleration will give the Schwarzschild metric. Christoffel symbols are not required.

Is a “reducing tensor” mathematically valid?
Title: Re: Can a tensor be represented as the average of vector triple products?
Post by: PmbPhy on 13/01/2020 17:49:38
The answer is no. And only some tensors can be represented by vectors and only then as the tensor product of those vectors.