Associativity of Hadamard and matrix product

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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
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Hi,

Let us suppose we have three real matrices A, B, C and let \circ denote the Hadamard product, while AB is the conventional matrix product. Is this relation true for all A, B, C matrices:
C \circ (AB) = A( C\circ B)?
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:
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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.
 

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