- #1
keddelove
- 3
- 0
And again a question:
L is a field for which [tex] a \in L [/tex]. The matrix
[tex]
A = \frac{1}{2}\left( {\begin{array}{*{20}c}
1 & 1 & 1 & 1 \\
1 & a & { - 1} & { - a} \\
1 & { - 1} & 1 & { - 1} \\
1 & { - a} & { - 1} & a \\
\end{array}} \right)
[/tex]
has the characteristic polynomial
[tex]
x^4 - \left( {a + 1} \right)x^3 + \left( {a - 1} \right)x^2 + \left( {a + 1} \right)x - a
[/tex]
I need to show that this information is correct for a=1 in any field.
My problem is that when i calculate the polynomial for a=-1 I end up with another characteristic polynomial than the one given. Maybe I'm going about it the wrong way. Suggestions or pointers are very welcome
L is a field for which [tex] a \in L [/tex]. The matrix
[tex]
A = \frac{1}{2}\left( {\begin{array}{*{20}c}
1 & 1 & 1 & 1 \\
1 & a & { - 1} & { - a} \\
1 & { - 1} & 1 & { - 1} \\
1 & { - a} & { - 1} & a \\
\end{array}} \right)
[/tex]
has the characteristic polynomial
[tex]
x^4 - \left( {a + 1} \right)x^3 + \left( {a - 1} \right)x^2 + \left( {a + 1} \right)x - a
[/tex]
I need to show that this information is correct for a=1 in any field.
My problem is that when i calculate the polynomial for a=-1 I end up with another characteristic polynomial than the one given. Maybe I'm going about it the wrong way. Suggestions or pointers are very welcome