How Does Matrix Inversion Affect Diagonal Transformation?

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The discussion focuses on the mathematical implications of matrix inversion and diagonal transformation, specifically examining the expression A-1DAT where D is a diagonal matrix. Participants clarify that if the components of matrix A are integers and its determinant equals 1, then the components of A-1 will also be integers. The conversation emphasizes the need for additional context regarding the relationship between matrices A, D, and their transformations to provide a complete answer.

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  • Understanding of matrix multiplication and properties
  • Familiarity with matrix inversion techniques
  • Knowledge of diagonal matrices and their characteristics
  • Basic concepts of determinants in linear algebra
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Students and professionals in mathematics, particularly those studying linear algebra, matrix theory, and transformations. This discussion is beneficial for anyone looking to deepen their understanding of matrix operations and their implications in various mathematical contexts.

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1. What is the value of the following matrix multiplication




2. [tex]A^{-1}DA^{T}=?[/tex]
D is diagonal matrix




3. and how to find D to make [tex]a_i C Z[/tex]


4. [tex]A^{-1}DA^{T}[/tex]


[tex]a_i[/tex] is elements of [tex]A^{-1}[/tex]
My head really aches, please help
 
Last edited:
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C is "belongs to" Z, I mean

I can't write a \belongto
 
You want the components of A-1 integers? I'm not sure what your question is. If the components of A itself are integers and A has determinant = 1, then the components of A-1 are integers. D has nothing to do with that- especially since you haven't told us anything about ADA-1. Is there some condition on that?

Oh, and [itex]a_n \in Z[/itex] is written [ itex ] a_n\in Z[ /itex ], without the spaces, of course.
 

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