I am just starting to become familiar with Tensors (most familiar with Moment of Inertia Tensor & Spring Constant Tensor), I am trying to understand the fundamental nature of them (as High-Level explanation as possible would be preferred)..
So a zeroth-order tensor is just a scalar.. A first-order tensor is a scalar and a direction (orientation)..
If a second-order tensor can be represented as a n x n matrix, it has scalar aspects, respective directions, but what is the third aspect that differentiates it from a 1st-order tensor?
I'm sure I am exposing some fundamental misunderstandings about Tensors, so any clarification is highly appreciated.
Given that you seem to be interested in physics, I will give you an answer that is in accordance with how every physics class I have dealt with thinks about tensors.
Basically, the order of a tensor is how many indices you need to specifiy the object. For a scalar, there is no index. First order means I need one index to go across the vector. Second order means I have a table of values, rows and columns.