Eigenvalues Polinomial???

Hello... Good Day.
I Have A Problem With Eigenvalues polinomial characteristic.

I've read some books to get eigenvalues.

If A=2x2:
a b
c d

then

polinomial is: lambda^2 - (a+b)lambda + det(A)

So

If A=3x3

a b c
d e f
g h i

polinomial is: -lambda^3 + (a+b+c) lambda^2 - (db+gc+hf-ae-ei) lambda + det(A)

so polinomial of eigenvalues is:
(-1)^n lambda^n + (-1)^(n-1) S1 lambda^(n-1) + (-1)^(n-2) Sk lambda^(k) + Sn

Where:
n=matrix dimension
s1=trace(A)
Sn=det(A)

I wanna ask how to get Sk?

If I have 4 dimension:

a b c d
e f g h
i j k l
m n o p

Thanks.
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