•A 4×4 Example

In[1]:=

A = (0 2 1 -2) ; -2 2 -2 0 -2 5 4 -4 3 6 -6 -6

In[2]:=

p[λ_] = Det[A - λ I _ 4]

Out[2]=

102 λ - 30 λ^2 + λ^4

In[3]:=

Factor[p[λ]]

Out[3]=

λ (102 - 30 λ + λ^3)

In[4]:=

Solve[p[λ] == 0, λ]

Out[4]=

{{λ -> 0}, {λ -> -10/(51 - 1601^(1/2))^(1/3) - (51 - 1601^(1/2))^(1/3)}, {λ -> (5 (1 + i 3^(1/2)))/(51 - 1601^(1/2))^(1/3) + 1/2 (1 - i 3^(1/2)) (51 - 1601^(1/2))^(1/3)}, {λ -> (5 (1 - i 3^(1/2)))/(51 - 1601^(1/2))^(1/3) + 1/2 (1 + i 3^(1/2)) (51 - 1601^(1/2))^(1/3)}}

In[5]:=

N[Solve[p[λ] == 0, λ]]

Out[5]=

{{λ -> 0.`}, {λ -> -6.721284839635205`}, {λ -> 3.3606424198176024` + 1.9702163387893539` i}, {λ -> 3.3606424198176024` - 1.9702163387893539` i}}

Converted by Mathematica  (November 21, 2002)