Find all 2 by 2 matrices that are orthogonal and also symmetric. Which two numbers can be eigenvalues of those two matrices?

ka1leE 2020-12-01 Answered
Find all 2 by 2 matrices that are orthogonal and also symmetric. Which two numbers can be eigenvalues of those two matrices?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

d2saint0
Answered 2020-12-02 Author has 89 answers

To find: 2×2 matrices that are orthogonal and also symmetric and two numbers that can be eigenvalues of that 2×2 matrices.
All 2×2 matrices that are orthogonal and also symmetric are as shown below:
[[cosθ,sinθ],[sinθ,cosθ]] and [[cosθ,sinθ],[sinθ,cosθ]]
And the two numbers that can be eigenvalues of the above 2×2 matrices are +-1

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more