数学试题讲解

已知矩阵

A = (\begin{array}{lll} a & a & b \\ a & b & a \\ b & a & a \end{array}) (a b \neq 0)

的正、负惯性指数相同，则

A

相似于

(\begin{array}{ccc} a & 0 & 0 \\ 0 & - a & 0 \\ 0 & 0 & 0 \end{array})

(\begin{array}{ccc} 2 a & 0 & 0 \\ 0 & - 2 a & 0 \\ 0 & 0 & 0 \end{array})

(\begin{array}{ccc} 3 a & 0 & 0 \\ 0 & - 3 a & 0 \\ 0 & 0 & 0 \end{array})

(\begin{array}{ccc} 4 a & 0 & 0 \\ 0 & - 4 a & 0 \\ 0 & 0 & 0 \end{array})