What property must a real square matrix have to be guaranteed an orthonormal basis of eigenvectors?
Show answer
Symmetric
The Spectral Theorem for real matrices states that a matrix is symmetric if and only if it is orthogonally diagonalizable. This means its eigenvectors are mutually perpendicular and its eigenvalues are all real numbers.
Also asked as:
- According to the Spectral Theorem, what property of a real matrix ensures it is orthogonally diagonalizable?