ComplexevlakReIm

Lineaire afbeelding gedefinieerd door de matrix

a_{21} = -0.8660254037844386 (slider from -5 to 5, step 0.1)
a_{12} = 0.8660254037844386 (slider from -5 to 5, step 0.1)
a_{22} = 0.5 (slider from -5 to 5, step 0.1)
a_{11} = 0.5 (slider from -5 to 5, step 0.1)
e_y = (0, 1)
O = (0, 0)
e_x = (1, 0)
Z_v: e_x + (2 * e_y)
v = Vector(O, Z_v)
Z_2 = (0.5, 1)
Z'_v: ((a_{11} * x(v)) + (a_{12} * y(v)), (a_{21} * x(v)) + (a_{22} * y(v)))
v' = Vector(O, Z'_v)
text2: "\bar v =\left( \begin{array}{c}" + (x(Z_v)) + "\\ " + y(Z_v) + " \end{array} \right)"
text6: "\bar{v}'= A \bar v = \left( \begin{array}{cc} " + a_{11} + " & " + a_{12} + "  \\ " + a_{21} + " & " + a_{22} + "  \end{array} \right) \left(\begin{array}{c} " + x(v) + " \\ " + y(v) + " \end{array}\right)=\left( \begin{array}{c}" + x(Z'_v) + "\\ " + y(Z'_v) + " \end{array} \right)"
w: e_x + e_y
z: (2 * e_x) + e_y
Z_w: w
Z_z: z
origineel, z_z, z_v, z_w = Polygon(Z_v, Z_w, Z_z)
Z'_w: ((a_{11} * x(w)) + (a_{12} * y(w)), (a_{21} * x(w)) + (a_{22} * y(w)))
Z'_z: ((a_{11} * x(z)) + (a_{12} * y(z)), (a_{21} * x(z)) + (a_{22} * y(z)))
beeld, z'_z, z'_v, z'_w = Polygon(Z'_v, Z'_w, Z'_z)
text5: "A = \left( \begin{array}{cc} a_{11}  & a_{12} \\ a_{21} & a_{22} \end{array} \right) =\left( \begin{array}{cc} " + (LaTeX[a_{11}]) + " & " + LaTeX[a_{12}] + "\\ " + LaTeX[a_{21}] + "& " + LaTeX[a_{22}] + "  \end{array} \right)"