Is the Inverse of a Diagonal Matrix Simply the Inverse of Its Elements?

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Discussion Overview

The discussion revolves around the properties of diagonal matrices, specifically whether the inverse of a diagonal matrix can be determined by taking the inverses of its individual elements. The scope includes theoretical exploration and mathematical reasoning.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant questions if the inverse of a diagonal matrix is simply the inverses of its elements.
  • Another participant introduces a different matrix (a 2 by 2 matrix with all entries as 1) and expresses confusion regarding the context of diagonal versus symmetric matrices.
  • A third participant suggests a method involving multiplication of a diagonal matrix with another matrix, implying a relationship but not providing a definitive conclusion.
  • A fourth participant expresses gratitude, indicating engagement but not contributing further to the technical discussion.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants raise different points and questions without resolving the initial inquiry about diagonal matrices.

Contextual Notes

There are potential limitations in understanding the properties of diagonal versus symmetric matrices, as well as the implications of matrix multiplication in this context.

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is the inverse of a diagonal matrix always just calculated by taking the inverses of each number in the matrix?
 
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What is the inverse of the 2 by 2 matrix all of whose entries are 1?

For some reason, I read "symmetric matrices" where the question was about "diagonal matrices".
 
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Take a diagonal matric, mutliply it by the one you just made, what's the answer?
 
thank you very much!
 

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