Associativity of Hadamard and matrix product

  • Context: Graduate 
  • Thread starter Thread starter Zoli
  • Start date Start date
  • Tags Tags
    Matrix Product
Click For Summary
SUMMARY

The discussion centers on the relationship between the Hadamard product and the conventional matrix product involving three real matrices A, B, and C. It is established that the equation C ∘ (AB) = A(C ∘ B) does not hold true for all matrices. The participants seek to explore alternative relationships that can exist between these two types of matrix operations, indicating a need for further investigation into their properties.

PREREQUISITES
  • Understanding of matrix operations, specifically Hadamard and conventional matrix products.
  • Familiarity with real matrices and their properties.
  • Basic knowledge of linear algebra concepts.
  • Experience with mathematical proofs and counterexamples.
NEXT STEPS
  • Research the properties of the Hadamard product in linear algebra.
  • Explore alternative relationships between matrix operations, focusing on associative and distributive properties.
  • Study examples of matrices where the Hadamard and conventional products interact.
  • Investigate the implications of matrix products in various applications, such as machine learning and data analysis.
USEFUL FOR

Mathematicians, students of linear algebra, and anyone interested in the properties of matrix operations will benefit from this discussion.

Zoli
Messages
19
Reaction score
0
Hi,

Let us suppose we have three real matrices [itex]A, B, C[/itex] and let [itex]\circ[/itex] denote the Hadamard product, while [itex]AB[/itex] is the conventional matrix product. Is this relation true for all [itex]A, B, C[/itex] matrices:
[tex]C \circ (AB) = A( C\circ B)?[/tex]
I looked at it more thoroughly and I realized that this assumption is not true. But then what relation can be created between matrix product and Hadamard product?
Thanks,
Zoli
 
Last edited:
Physics news on Phys.org
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
I couldn't solve it, so the post can be reworded.
 

Similar threads

Graduate Hermitian of product of two matrices
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Consistent matrix index notation when dealing with change of basis
  • · Replies 12 ·
Replies
12
Views
2K
Graduate The meaning of ##(ict, x_1,x_2,x_3)##
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Eigenvectors and matrix inner product
  • · Replies 1 ·
Replies
1
Views
3K
Graduate 4th order tensor inverse and double dot product computation
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Solutions of Matrix Equation A X B^T = C
  • · Replies 1 ·
Replies
1
Views
3K
Product of two boosts and then two inverse boosts is rotation matrix
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad Generalized Eigenvalues of Pauli Matrices
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Understanding Matrix Multiplication: A Vector-Based Explanation
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad Image of a Matrix and symmetric matrix
  • · Replies 3 ·
Replies
3
Views
3K