Are Cube Matrices the Next Frontier in Linear Algebra?

Click For Summary

Discussion Overview

The discussion revolves around the concept of cube matrices, or three-dimensional matrices, and their potential significance in linear algebra. Participants explore whether such mathematical entities exist and what benefits might arise from studying them, particularly in relation to tensors and their applications in physics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions the existence and utility of cube matrices, suggesting that studying them as a whole might yield insights.
  • Another participant asserts that cube matrices do exist and are useful, referencing tensors as a related concept that has historical significance in physics.
  • A later reply indicates that the questioner has encountered tensors previously but only in a superficial manner, highlighting a gap in understanding.
  • Another participant clarifies that scalars, vectors, and matrices are specific cases of tensors with varying dimensions, which may imply a broader framework for understanding cube matrices.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the utility and implications of cube matrices. While some assert their existence and relevance, others express uncertainty about their benefits and understanding.

Contextual Notes

The discussion lacks rigorous definitions and mathematical formalism regarding cube matrices and tensors, which may affect the clarity of the arguments presented.

Vorde
Messages
786
Reaction score
0
I just had my last Linear Algebra class, and I didn't get a chance to ask the one question that has been bugging me ever since we started in earnest with matrices.

Why aren't there cube matrices? I mean, mathematical entities where numbers are 'laid out' in 3d not in 2d (not quite mathematically rigorous, but you get the idea). Obviously one could do this with successive matrices, but I wonder if more is to be gained by studying this object as a whole.

Is this a thing? Is there an obvious reason I'm missing as to why there is nothing to gain by doing this?
 
Physics news on Phys.org
There are, and they certainly are useful; physics wouldn't have got much beyond Newton without them. Google "tensors".
 
Huh, you know I've known about tensors for a while but in a purely pop-science way (the only actual tensors I've been exposed to were in a five-minute digression by my teacher briefly explaining them), I hadn't ever been told to think of them that way!
 
That's a shame, although you have actually been exposed to tensors for some time. Ordinary numbers (scalars), vectors and matrices are just special cases of tensors with 0, 1 and 2 dimensions respectively.
 

Similar threads

High School What unique contributions to math did linear algebra make?
  • · Replies 19 ·
Replies
19
Views
4K
Undergrad What is the proper matrix product?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad What are the differences between matrices and tensors?
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Looking for learning resources for Clifford Algebra
  • · Replies 1 ·
Replies
1
Views
754
Undergrad The Price of Beer - Linear Algebra Problem
  • · Replies 44 ·
2
Replies
44
Views
5K
Undergrad Meaning of "passage to the quotient"?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Linear algebra ( symmetric matrix)
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Proving linear independence of two functions in a vector space
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Passive Transformation and Rotation Matrix
  • · Replies 1 ·
Replies
1
Views
4K
High School Easy definition of linear algebra
  • · Replies 16 ·
Replies
16
Views
8K