Diagonalizable Matrices: Proof of AB being Diagonalizable

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SUMMARY

Diagonalizable matrices A and B of the same size guarantee that the product AB is also diagonalizable. This conclusion is based on the properties of eigenvalues and eigenvectors inherent in diagonalizable matrices. The discussion emphasizes the importance of understanding the definition of diagonalizable matrices to effectively prove this statement. The proof relies on the fact that if A and B can be expressed in diagonal form, their product retains this property.

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  • Understanding of diagonalizable matrices
  • Knowledge of eigenvalues and eigenvectors
  • Familiarity with matrix multiplication
  • Basic linear algebra concepts
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  • Study the properties of eigenvalues and eigenvectors in detail
  • Learn about the diagonalization process of matrices
  • Explore proofs related to matrix products and their diagonalizability
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Homework Statement


Prove if A and B are two diagonalizable matrices of the same size, then AB is also diagonalizable.


Homework Equations





The Attempt at a Solution

 
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timberchris said:

Homework Statement


Prove if A and B are two diagonalizable matrices of the same size, then AB is also diagonalizable.


Homework Equations





The Attempt at a Solution


Welcome to Physics Forums!

Being that this is your first post, you probably haven't taken time to look at the rules, which say that you need to make an attempt at a solution before we can help.

What is the definition of a "diagonalizable" matrix? That's pertinent here.
 

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