Matrix notation for vector stacking

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To stack a row vector X vertically N times into a matrix Y, one can use matrix notation by multiplying a column vector of ones by the row vector. The expression (1,1,...,1)^T * (x_1,...,x_L) effectively creates the desired matrix format. This approach simplifies the process without the need for summations or additional operators. The solution is straightforward and efficient for vector stacking in matrix notation. The discussion concludes with appreciation for the simplicity of the solution.
hadron23
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Hello,

I have a row vector defined as,

X=\{x_1,x_2,\ldots,x_L\}
I wish to "stack" this vector vertically, a total of N times, such that the result is a matrix of the form,

\begin{align}Y = \left[ \begin{array}{cccc}<br /> x_1 &amp; x_2 &amp; \ldots &amp; x_L \\<br /> x_1 &amp; x_2 &amp; \ldots &amp; x_L \\<br /> . &amp; . &amp; . &amp; .\\<br /> . &amp; . &amp; . &amp; .\\<br /> . &amp; . &amp; . &amp; .\\<br /> x_1 &amp; x_2 &amp; \ldots &amp; x_L \end{array} \right]<br /> \end{align}
I want to write this in matrix notation, that is, using only vectors and matrices, and not any summations or other operators. I am not sure how to do this cleanly, any help would be greatly appreciated :)

Thank you.
 
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Hi hadron23! :smile:

What about

(1,1,...,1)^T.(x_1,...,x_n)
 
In hindsight, this is stupidly simple. Thanks!
 
I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

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