**[1]** The eigenvalues of $ A $ are $ (1,-1, i,-i) $.\n",
"\n",
"

**[2]** The correct way to argue this is by induction. Suppose that\n",
"$ x_t $ is Gaussian. Then [(20.1)](#equation-st-space-rep) and\n",
"[(20.10)](#equation-lss-glig) imply that $ x_{t+1} $ is Gaussian. Since $ x_0 $\n",
"is assumed to be Gaussian, it follows that every $ x_t $ is Gaussian.\n",
"Evidently, this implies that each $ y_t $ is Gaussian."
]
}
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