Let the function $f ( x ) = \mathrm { e } ^ { x } + a \mathrm { e } ^ { - x }$ ($a$ is a constant). If $f ( x )$ is an odd function, then $a =$ $\_\_\_\_$; if $f ( x )$ is an increasing function on $\mathbb { R }$, then the range of $a$ is $\_\_\_\_$.