Computing a kronecker product of two matrices

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SUMMARY

The discussion focuses on computing the Kronecker product of two matrices, specifically 2x2 matrices, and implementing this in Fortran. The user seeks an efficient algorithm to generate a 4x4 matrix from the input matrices without resorting to creating a rank 4 tensor, which is cumbersome. References to MATLAB's implementation of the Kronecker product are provided as a potential resource for understanding the algorithm. The conversation emphasizes the importance of clarity in identifying specific challenges faced during implementation.

PREREQUISITES
  • Understanding of Kronecker products in linear algebra
  • Familiarity with matrix operations in Fortran
  • Basic knowledge of tensor concepts
  • Experience with MATLAB for comparative analysis
NEXT STEPS
  • Research the algorithm for computing Kronecker products in Fortran
  • Explore MATLAB's function for Kronecker products, specifically the 'kron' function
  • Study tensor representations and their applications in programming
  • Investigate optimization techniques for matrix multiplication in Fortran
USEFUL FOR

Mathematicians, software developers, and engineers working with matrix computations, particularly those implementing algorithms in Fortran or transitioning from MATLAB.

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Does anyone know an algorithm for computing kronecker products of two matrices? It's probably not that hard, but I feel like my head is about to explode ATM, so if you can help me out that'd be cool. I want to implement this in fortran... I'll give you an example; Say I want compute the kronecker product between two 2x2 matrices (http://en.wikipedia.org/wiki/Tensor_product#Kronecker_product_of_two_matrices). I know that in the end the result of the product is a tensor, so the straightforward way to do this would be to create a rank 4 tensor in the program, but that's unwieldy... What I want is to generate a matrix (4x4), starting from these 2x2 matrices.
 
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It seems to me that the definition you linked to has all the information you need. You probably just need to take a break, do something else for a couple of hours, and return to it with a fresh mind. If you have already tried that, then you should probably be more specific about what's causing you problems.
 

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