Matrix notation for vector stacking

In summary, the conversation is about creating a matrix by vertically stacking a row vector multiple times. The desired matrix should have the same row vector repeated N times. The speaker is looking for a clean way to write this in matrix notation without using summations or other operators. The solution proposed is to use a transpose of a vector of all ones multiplied by the original row vector.
  • #1
hadron23
28
1
Hello,

I have a row vector defined as,

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

[tex]\begin{align}Y = \left[ \begin{array}{cccc}
x_1 & x_2 & \ldots & x_L \\
x_1 & x_2 & \ldots & x_L \\
. & . & . & .\\
. & . & . & .\\
. & . & . & .\\
x_1 & x_2 & \ldots & x_L \end{array} \right]
\end{align}[/tex]
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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  • #2
Hi hadron23! :smile:

What about

[tex](1,1,...,1)^T.(x_1,...,x_n)[/tex]
 
  • #3
In hindsight, this is stupidly simple. Thanks!
 

1. What is matrix notation for vector stacking?

Matrix notation for vector stacking is a mathematical representation of arranging multiple vectors into a single matrix. It is commonly used in linear algebra and other fields of science for data organization and manipulation.

2. How is vector stacking different from vector concatenation?

Vector stacking involves arranging multiple vectors into a single matrix, while vector concatenation involves combining multiple vectors into a longer vector. In vector stacking, the resulting matrix will have the same number of rows as the number of vectors being stacked, while in vector concatenation, the resulting vector will have a length equal to the sum of the lengths of the individual vectors.

3. What is the purpose of using matrix notation for vector stacking?

The main purpose of using matrix notation for vector stacking is to simplify the representation and manipulation of multiple vectors. It allows for easier and more efficient calculations, especially when dealing with large datasets.

4. How is matrix notation for vector stacking written?

Matrix notation for vector stacking is typically written as [v1 v2 v3 ... vn], where v1, v2, v3, and vn denote the individual vectors being stacked. It can also be written as [v1; v2; v3; ...; vn], where the vectors are stacked vertically.

5. Can vectors with different dimensions be stacked using matrix notation?

No, vectors with different dimensions cannot be stacked using matrix notation. The vectors being stacked must have the same number of elements, i.e. the same dimension, in order to be represented as a matrix.

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