Computing a kronecker product of two matrices

In summary, the conversation discusses the implementation of a kronecker product algorithm for two matrices, with one person seeking help and another providing a resource for assistance. They also mention the use of a rank 4 tensor and the potential difficulty in implementing the algorithm in Fortran. The linked definition of the kronecker product is suggested as a helpful resource, and taking a break is recommended for a fresh perspective. A Matlab function for the kronecker product is also shared.
  • #1
Amok
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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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  • #2
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.
 

What is a kronecker product?

A kronecker product is a mathematical operation that takes two matrices and produces a new matrix. It is denoted by the symbol ⊗ and is used in linear algebra and signal processing.

How is a kronecker product computed?

A kronecker product is computed by multiplying each element of one matrix by the entire second matrix, resulting in a new matrix that is the size of the first matrix multiplied by the size of the second matrix.

What is the purpose of computing a kronecker product?

The kronecker product is used to create a larger matrix from two smaller matrices. It is often used in statistics and data analysis to model complex relationships between variables.

What are the properties of a kronecker product?

The kronecker product is distributive, associative, and commutative. It also follows the rule (A ⊗ B)T = AT ⊗ BT, where T denotes the transpose of a matrix.

What are some practical applications of computing a kronecker product?

The kronecker product is used in various fields such as signal processing, computer graphics, and image analysis. It is also used in machine learning and deep learning algorithms for feature extraction and data manipulation.

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