$\mbox{Konstruktive Ermittlung der Eigenwerte und Eigenvektoren}

$P$

$Q$

$A=\left(\begin{array}{c}a & b\ b & c\end{array}\right)$

$\mbox{jener linearen Abbildung \varphi, welche durch}$

$\varphi: \mathbb{R}^2 \rightarrow \mathbb{R}^2, \mathfrak{x}\mapsto \mathfrak{y}=\varphi(\mathfrak{x})=A\cdot \mathfrak{x}$

\mbox{mit symmetrischer Abbildungsmatrix}

$\mbox{vermittelt wird, Dr. Robert Resel, 2015}$

a = 2.6 (slider from -10 to 10, step 0.1)
b = 2.8 (slider from -10 to 10, step 0.1)
c = 1.5 (slider from -10 to 10, step 0.1)
P: ((-b), a)
Q: (b, c)
d = Segment(P, Q)
M = Intersect(d, yAxis)
X': (a, b)
O = (0, 0)
x' = Vector(O, X')
y' = Vector(O, Q)
k = Circle(M, P)
u = -1.8 (slider from -10 to 10, step 0.1)
v_1 = 1 (slider from -10 to 10, step 0.1)
U: (u, v_1)
w' = Vector(O, U)
au: (a * u)
bv: (b * v_1)
bu: (b * u)
cv: (c * v_1)
A: (au + bv, bu + cv)
w = Vector(O, A)
Y_1, Y_2 = Intersect(k, yAxis)
e_2 = Vector(Y_2, Q)
e_1 = Vector(P, Y_2)