Linear algebra in $\mathbb{Q}$

Algebra Level 3

True or False?

For all $n$ , if $A\in S_n(\mathbb{Q})$ , then A is diagonalizable .

Notation : $S_n(\mathbb{Q})$ denotes the space of rational symmetric matrices

False True

1 solution

Victor Moreno Diaz
Aug 3, 2016

If $n=2$ , just take $A=\begin{pmatrix} 1/2 &5/4 \\ 5/4 &3/2 \end{pmatrix}$ .