  This short note presents upper bounds of the expectations of the largest
singular values/eigenvalues of various types of random tensors in the
non-asymptotic sense. For a standard Gaussian tensor of size
$n_1\times\cdots\times n_d$, it is shown that the expectation of its largest
singular value is upper bounded by $\sqrt {n_1}+\cdots+\sqrt {n_d}$. For the
expectation of the largest $\ell^d$-singular value, it is upper bounded by
$2^{\frac{d-1}{2}}\prod_{j=1}^{d}n_j^{\frac{d-2}{2d}}\sum^d_{j=1}n_j^{\frac{1}{2}}$.
We also derive the upper bounds of the expectations of the largest
Z-/H-($\ell^d$)/M-/C-eigenvalues of symmetric, partially symmetric, and
piezoelectric-type Gaussian tensors, which are respectively upper bounded by
$d\sqrt n$, $d\cdot 2^{\frac{d-1}{2}}n^{\frac{d-1}{2}}$, $2\sqrt m+2\sqrt n$,
and $3\sqrt n$.
