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Conjugacy class structure
| <math>A</matH> is the identity, <math>v \ne 0</math> || <math>\{ 1,1 \}</math> || <math>(x - 1)^2</math> || <math>x - 1</math> || <math>q^2 - 1</math> || 1 || <matH>q^2 - 1</math> || Yes || Yes
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| <math>A</math> is diagonalizable over <math>\mathbb{F}_q</math> with equal diagonal entries not equal to 1, hence a scalar. The value of <matH>v</math> does not affect the conjugacy class. || <math>\{a,a \}</math> where <math>a \in \mathbb{F}_q^\ast \setminus \{ 1 \}</math> || <math>(x - a)^2</math> where <math>a \in \mathbb{F}_q^\ast\setminus \{ 1 \}</math> || <math>x - a</math> where <math>a \in \mathbb{F}_q^\ast\setminus \{ 1 \}</math> || <math>q^2</math> || <math>q - 2</math> || <math>q^2(q - 2)</math> || Yes || Yes
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| <math>A</math> is diagonalizable over <math>\mathbb{F}_{q^2}</math>, not over <math>\mathbb{F}_q</math>. Must necessarily have no repeated eigenvalues. The value of <math>v</matH> does not affect the conjugacy class. || Pair of conjugate elements of <math>\mathbb{F}_{q^2}</math> || <math>x^2 - ax + b</math>, irreducible || Same as characteristic polynomial || <math>q^3(q - 1)</math> || <math>q(q - 1)/2 = (q^2 - q)/2</math> || <math>q^4(q-1)^2/2</math> || Yes || No
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