Is there a notation for a matrix which columns are the same vector?
$$ x = \left[\begin{array}{ccc}x_1 & x_2 & x_3\end{array}\right]^{T} \\ y = \left[\begin{array}{ccc}x & x & x\end{array}\right] $$
Is there a proper notation for $y$?
The notation you have for $y$ is fine. It's common block matrix notation.
Sometimes I've seen it wrote like this $$\left(\begin{matrix} |&|&|\\x&x&x\\|&|&|\end{matrix}\right)$$ The form you suggested doesn't seems right to me, but I could be wrong!
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The notation you have for $y$ is fine. It's common block matrix notation.