Kronecker Product: Solving AA` with w & D

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SUMMARY

The discussion centers around the mathematical problem of expressing the matrix product AA' = (wDD'w)(wDD'w) as a Kronecker product of two matrices. The matrices involved are w, an n x n symmetric matrix, and D, an n x m matrix. Participants highlight the challenge of dimension compatibility when attempting to multiply a Kronecker product with AA', indicating that the operation may not be feasible due to dimensional constraints.

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  • Understanding of matrix multiplication and properties of symmetric matrices.
  • Familiarity with the Kronecker product and its applications in linear algebra.
  • Knowledge of matrix dimensions and how they affect operations.
  • Basic concepts of matrix transposition and its implications in matrix products.
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  • Research the properties of the Kronecker product in linear algebra.
  • Explore dimensionality constraints in matrix operations.
  • Study symmetric matrices and their characteristics in matrix equations.
  • Investigate alternative methods for expressing matrix products in terms of Kronecker products.
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Mathematicians, data scientists, and anyone involved in advanced linear algebra or matrix theory who seeks to understand the complexities of matrix operations and Kronecker products.

Shurid
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Hi everyone,

Please help me with this problem.

Suppose w be a n x n symmetric matrix and D be n x m matrix.

Let A=wDD`w.

Is it possible to write the matrix, AA`= (wDD`w)(wDD`w) as the kronecker product of any two matrices?

Thanks in advance.
 
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Every matrix B is a Kronecker product [itex]X\otimes Y[/itex], where X=B and Y is 1x1 identity matrix.
 
Thanks a lot Arkazad. You are right. However, what I want is to multiply

(A kronecker product B) by (AA`), where B is also a n x n matrix. You observe that this is not even defined. I don't know may be this is impossible, because I can not change the dimension of AA`.

Any further idea?
 

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