Explain why matrix multiplication is not commutative.

Click For Summary

Discussion Overview

The discussion centers around the non-commutative nature of matrix multiplication, exploring the conditions under which matrix products are defined and the implications of these definitions. The scope includes theoretical aspects and potential applications in mathematical contexts.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested, Homework-related

Main Points Raised

  • Some participants note that matrix multiplication is defined only for certain rectangular matrices, with the product AB being defined if the number of columns in A equals the number of rows in B, while BA may not be defined.
  • One participant provides an example with square matrices, suggesting that generally AB ≠ BA for all values of i, attributing this to the definition of matrix multiplication.
  • Another participant questions the intent behind the inquiry, implying that it may be related to homework.
  • A participant emphasizes the need to clarify whether the question is a homework issue before proceeding with further discussion.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the question, with some focusing on the mathematical definitions and others questioning the context of the inquiry. No consensus is reached regarding the intent behind the question or the depth of explanation required.

Contextual Notes

The discussion highlights limitations related to the definitions of matrix multiplication and the conditions under which products are defined, but does not resolve these complexities.

xsgx
Messages
29
Reaction score
0
The title says it all.

Commutative* sorry
Mod note: fixed title.
 
Last edited by a moderator:
Physics news on Phys.org
Let A = [aij] and B = [ajk] where j ≠ k, then AB is defined, but BA is not.

But consider the case where i = j = k, so that A = [ai] and B = [ai] are square matrices.

Then, take for example i = 2 and calculate AB and BA. What do you find?

Generally, AB ≠ BA, for all values of i. It just stems from the definition of matrix multiplication.
 
Matrix multiplication is defined only for certain rectangular matrices A and B. The matrix product AB is defined only if the number of columns in A is equal to the number of rows in B. Assuming this condition is met, the product AB is defined, but the product BA may not be.
 
h6ss and SteamKing,
Please hold off further comments until I can ascertain whether this is a homework question. If it is, it was posted in the wrong section with no efforts shown.
 

Similar threads

Undergrad In 4x4 matrix when does row swapping not affect eigenvaluess?
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad What is the proper matrix product?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad The Multiplication Table is a Hermitian Matrix
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad Jacobi matrix diagonalization problems
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Why is the dot product equivalent to matrix multiplication?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad What does the multiplication of matrix represents?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Why Use Gram-Schmidt to Make a Unitary Matrix?
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad Is the Cauchy stress tensor really a tensor?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Transformation of Tensor Components
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Matrix diagonalization algorithm
  • · Replies 5 ·
Replies
5
Views
3K