Symmetric matrices

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Symmetric matrices have nice properties. We show that all the eigenvalues of a real symmetric matrix are real, and the eigenvectors corresponding to different eigenvalues are orthogonal. We further show the diagonalization and the spectral decomposition of a symmetric matrix.

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  1. Brunei Math Club
  2. Mathematics
  3. linear algebra
  4. symmetric matrix
  5. spectral decomposition
  6. diagonalization
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The eigen basis is dual to the standard basis -- conjugacy is dual, spectral decomposition.
The integers are self dual as they are their own conjugates.
"Always two there are" -- Yoda.
Real is dual to imaginary -- complex numbers are dual.
Antipodal points identify for the rotation group SO(3) -- stereographic projection.

hyperduality