Needs["VisualDSolve`"];

\(\(linpend = 
      PhasePlot[{\(x'\)[t] == y[t], \(y'\)[t] == \(-y[t]\) + x[t]}, 

        	{x[t], y[t]}, 
	{t, 0, 100}, 
	{x, \(-1\), 1}, 

        	{y, \(-1\), 1}, 
		VectorField -> True, FieldLogScale -> 9, 
        FieldColor -> Blue, 
			FieldThickness -> AbsoluteThickness[2], 

        		\ \ ShowEquilibria -> True, 
\ \ 	
        AxesLabel -> {"x", "y"}
	]; \)\)

\(\(linpend = 
      PhasePlot[{\(x'\)[t] == y[t], \(y'\)[t] == \(-y[t]\) + x[t]}, 

        	{x[t], y[t]}, 
	{t, 0, 100}, 
	{x, \(-1\), 1}, 

        	{y, \(-1\), 1}, 
		VectorField -> True, FieldLogScale -> 9, 
        FieldColor -> Blue, 
			FieldThickness -> AbsoluteThickness[2], 

        		\ \ ShowEquilibria -> True, 
\ \ 	
        AxesLabel -> {"x", "y"}, 
				
        Epilog -> {AbsoluteThickness[2], Red, 
            Line[{{1\/2\ \((1 - \@5)\), 1}, 
                \(-\ {1\/2\ \((1 - \@5)\), 1}\)\ }], 
            Line[{{1\/2\ \((1 + \@5)\), 1}\ , 
                \(-{1\/2\ \((1 + \@5)\), 1}\)\ }]}
	]; \)\)

Eigensystem[{{0, 1}, {1, -1}}]