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rotatedAxes[ angle_] := (H = With[{r = RotationMatrix[Pi/4]}, r . DiagonalMatrix[{1, 2}] . Inverse[r]]; f[{x_, y_}] = {x, y} . H . {x, y}; rotmat = RotationMatrix[angle]; xaxis = rotmat . {5, 0}; yaxis = rotmat . {0, 5}; Hdisp = Map[NumberForm[#, {3, 2}] &, N[Inverse[rotmat] . H . rotmat], {2}] // MatrixForm; ...


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Clear["Global`*"] rotatedAxes[angle_] := (H = With[{r = RotationMatrix[Pi/4]}, r . DiagonalMatrix[{1, 2}] . Inverse[r]]; f[{x_, y_}] = {x, y} . H . {x, y}; rotmat = RotationMatrix[angle]; xaxis = rotmat . {5, 0}; yaxis = rotmat . {0, 5}; Hdisp = Map[NumberForm[#, {3, 2}] &, N[Inverse[rotmat] . H . rotmat], {2}] // ...


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