已知实二次型 $f(x_{1}, x_{2}, x_{3}) = a\left(x_{1}^{2} + x_{2}^{2} + x_{3}^{2}\right) + 4x_{1}x_{2} + 4x_{1}x_{3} + 4x_{2}x_{3}$ 经正交变换 $\mathbf{x} = \mathbf{P}\mathbf{y}$ 可化成标准形 $f = 6y_{1}^{2}$ , 则 $a =$