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

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SUMMARY

The inverse of a diagonal matrix is indeed calculated by taking the inverses of each non-zero element in the matrix. For a 2x2 matrix where all entries are 1, the matrix is not invertible as its determinant is zero. The discussion highlights the importance of distinguishing between diagonal and symmetric matrices when considering matrix operations.

PREREQUISITES
  • Understanding of matrix operations, specifically matrix inversion.
  • Knowledge of diagonal matrices and their properties.
  • Familiarity with determinants and their role in matrix invertibility.
  • Basic linear algebra concepts, including symmetric matrices.
NEXT STEPS
  • Study the properties of diagonal matrices in linear algebra.
  • Learn about matrix determinants and their significance in determining invertibility.
  • Explore the concept of symmetric matrices and their characteristics.
  • Investigate practical applications of matrix inversion in computational tools like MATLAB or NumPy.
USEFUL FOR

Students of linear algebra, mathematicians, and anyone involved in computational mathematics or engineering who needs to understand matrix operations and their implications.

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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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