Orthogonal Diagonalization: An Example

We give an example of diagonalizing a symmetric 2x2 matrix. We prove that if a matrix is symmetric, then distinct eigenvalues have orthogonal (perpendicular) eigenvectors. When a matrix has columns which are mutually orthogonal, its inverse is its transpose. This allows us to quickly find the inverse of the eigenvector matrix and efficiently orthogonally diagonalize the matrix.
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