And again a question:(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Characteristic polynomial

**Physics Forums | Science Articles, Homework Help, Discussion**