Determinant of product of matrices

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SUMMARY

The determinant of the product of matrices is expressed as det(AB) = det(A)det(B), which can be proven using the Levi-Civita symbol. While the proof is not directly presented in "Linear Algebra" by Serge Lang, it utilizes the concept of permutation signs, which closely relates to the Levi-Civita symbol. This connection allows for a straightforward adaptation of the proof to incorporate the Levi-Civita symbol.

PREREQUISITES
  • Understanding of matrix operations and properties
  • Familiarity with determinants and their calculations
  • Knowledge of the Levi-Civita symbol and its applications
  • Basic concepts of permutations and their signs
NEXT STEPS
  • Study the Levi-Civita symbol and its role in linear algebra
  • Review the proof of the determinant product identity in "Linear Algebra" by Serge Lang
  • Explore advanced properties of determinants in relation to matrix theory
  • Learn about permutation groups and their significance in linear transformations
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Mathematicians, students of linear algebra, and anyone interested in advanced matrix theory and determinants.

LagrangeEuler
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Do you know where can I find proven identity
[tex]det(AB)=det(A)det(B)[/tex]
using Levi Civita symbol.
 
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You can find a proof in "Linear Algebra" by Lang. He doesn't exactly use the Levi-Civita symbol, but he rathers works with signs of permutations. But this is of course almost the same as the Levi-Civita symbol, so it should be very easy to rewrite the proof.
 

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