What is the theory behind elementary matrices?

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SUMMARY

Elementary matrices are defined in the form E(σ, u, v) = I - (1/σ)uvT, where I is the identity matrix. These matrices play a crucial role in linear algebra, particularly in transformations and matrix operations. Standard linear algebra textbooks provide comprehensive coverage of the theory behind elementary matrices, making them accessible for further study.

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  • Understanding of linear algebra concepts
  • Familiarity with matrix operations
  • Knowledge of identity matrices
  • Basic understanding of matrix transformations
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  • Research the properties of elementary matrices in linear algebra
  • Study matrix transformations and their applications
  • Explore specific linear algebra textbooks that cover elementary matrices
  • Learn about the role of elementary matrices in solving linear equations
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Students and professionals in mathematics, particularly those studying linear algebra, as well as educators seeking resources on elementary matrices.

stanley.st
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Hello,

I need to find some theory about elementary matrices. That are the matrices in the form

\mathbf{E}(\sigma,\mathbf{u},\mathbf{v})=\mathbf{I}-\frac{1}{\sigma}\mathbf{uv}^{T}

I can't find anywhere some theory about it. Can you give me some useful links?

Thank you so much...
 
Physics news on Phys.org
Hello stanley.st! :smile:

If you can't find a link, where did you come across this?

(it's not something I've seen before)
 
Any decent linear algebra book covers elementary matrices.
 

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