H = ( {
{Subscript[\[CurlyPhi], 1][x, t], -Subscript[
\!\(\*OverscriptBox[\(\[CurlyPhi]\), \(_\)]\), 2][x, t]},
{Subscript[\[CurlyPhi], 2][x, t], Subscript[
\!\(\*OverscriptBox[\(\[CurlyPhi]\), \(_\)]\), 1][x, t]}
} );
\[CapitalLambda] = ( {
{Subscript[\[Lambda], 1], 0},
{0, Subscript[
\!\(\*OverscriptBox[\(\[Lambda]\), \(_\)]\), 1]}
} );
A = ( {
{1, 0},
{0, 1}
} );
S = H.\[CapitalLambda].Inverse[H];
T = \[Lambda] A - S // MatrixForm
{Subscript[\[CurlyPhi], 1][x, t], -Subscript[
\!\(\*OverscriptBox[\(\[CurlyPhi]\), \(_\)]\), 2][x, t]},
{Subscript[\[CurlyPhi], 2][x, t], Subscript[
\!\(\*OverscriptBox[\(\[CurlyPhi]\), \(_\)]\), 1][x, t]}
} );
\[CapitalLambda] = ( {
{Subscript[\[Lambda], 1], 0},
{0, Subscript[
\!\(\*OverscriptBox[\(\[Lambda]\), \(_\)]\), 1]}
} );
A = ( {
{1, 0},
{0, 1}
} );
S = H.\[CapitalLambda].Inverse[H];
T = \[Lambda] A - S // MatrixForm