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        "Let $S$ be a $2\\times2$ symmetric matrix, with entries $s_{ij}$.  It it well known that any symmetric matrix may be diagonalized by an orthogonal similarity transformation. In symbols, for this special case, this implies we need to choose a value for $\\theta$ for which:$$ H^{\\mathsf{T}} S H =\\left[\\begin{array}{lr}\\cos \\theta & -\\sin \\theta \\\\sin \\theta & \\cos \\theta\\end{array} \\right]\\left[\\begin{array}{lr}s_{11} & s_{12} \\s_{21} & s_{22}\\end{array} \\right]\\left[\\begin{array}{rr}\\cos \\theta & \\sin \\theta \\-\\sin \\theta & \\cos \\theta\\end{array} \\right]",
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