Ker A Subset Ker B: Finding a Reference

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SUMMARY

The discussion centers on the algebraic relationship between the kernels of two matrices, A and B, specifically that Ker A is a subset of Ker B if and only if there exists a matrix M such that B = MA. The user seeks a reference to support this result in their paper, indicating that it is a classical result in linear algebra. They have a proof but require a citation from a textbook or academic paper to substantiate their claims.

PREREQUISITES
  • Understanding of linear algebra concepts, particularly matrix theory.
  • Familiarity with the definitions of kernel and image of a matrix.
  • Knowledge of matrix multiplication and its implications in linear transformations.
  • Experience with academic writing and citation practices in mathematics.
NEXT STEPS
  • Research classical linear algebra textbooks such as "Linear Algebra Done Right" by Sheldon Axler.
  • Explore academic papers on matrix theory that discuss kernel relationships.
  • Investigate online resources or lecture notes that cover the properties of linear transformations.
  • Look into mathematical forums or communities for additional references on kernel subset relationships.
USEFUL FOR

Mathematicians, students of linear algebra, and researchers looking for foundational references in matrix theory and kernel relationships.

agnes.gorge
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Hello,

I am trying to find a reference for the following results :

Let A and B be two matrices :
Ker A \subset Ker B if and only if there exists M such that B= MA

I already have a proof for this statement, but it looks like a classical algebraic result, so I'm looking for a reference to add in my paper, like a book or a paper..

Thanks in advance for any suggestions..
 
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I'm watching the knicks right now and admit i don't see it quite completely in my head, but this looks like a homework level question. so a reference would be in a beginning textbook.
 
Thank you for you help, I'll try to find such a book..
 

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