Matrix notation for vector stacking

Click For Summary
SUMMARY

The discussion focuses on the matrix notation for vertically stacking a row vector, specifically defined as X = {x₁, x₂, ..., xₗ}, into a matrix Y repeated N times. The solution proposed involves using the outer product of a column vector of ones, (1, 1, ..., 1)ᵀ, with the row vector (x₁, ..., xₗ). This approach effectively constructs the desired matrix Y without the need for summations or additional operators, demonstrating a clean and efficient method for vector stacking.

PREREQUISITES
  • Understanding of vector and matrix notation
  • Familiarity with outer products in linear algebra
  • Knowledge of matrix dimensions and operations
  • Basic proficiency in mathematical notation and expressions
NEXT STEPS
  • Study the properties of outer products in linear algebra
  • Learn about matrix operations and their applications in data manipulation
  • Explore vectorization techniques in programming languages like Python or MATLAB
  • Investigate advanced matrix decompositions and their uses in machine learning
USEFUL FOR

Mathematicians, data scientists, and anyone involved in linear algebra or matrix computations will benefit from this discussion, particularly those looking to optimize vector manipulations in their work.

hadron23
Messages
28
Reaction score
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}<br /> x_1 & x_2 & \ldots & x_L \\<br /> x_1 & x_2 & \ldots & x_L \\<br /> . & . & . & .\\<br /> . & . & . & .\\<br /> . & . & . & .\\<br /> x_1 & x_2 & \ldots & x_L \end{array} \right]<br /> \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.
 
Physics news on Phys.org
Hi hadron23! :smile:

What about

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

Similar threads

Undergrad Index notation of vector rotation
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Showing ##k[x_1,\ldots,x_n]/\mathfrak{a}## is finite dimensional
  • · Replies 40 ·
2
Replies
40
Views
5K
Undergrad Use of Laplacian operator in Operations Research Book
  • · Replies 6 ·
Replies
6
Views
3K
MHB -311.1.5.8 Ax=b in parametric vector form,
  • · Replies 7 ·
Replies
7
Views
1K
MHB Give a basis to get the specific matrix M
  • · Replies 34 ·
2
Replies
34
Views
3K
Graduate Vectors as geometric objects and vectors as any mathematical objects
  • · Replies 27 ·
Replies
27
Views
3K
Undergrad Change of Basis Matrix vs Transformation matrix in the same basis....
  • · Replies 12 ·
Replies
12
Views
5K
MHB System no/infinitely many solution(s)
  • · Replies 15 ·
Replies
15
Views
2K
MHB How do unit vectors and eigenvalues relate to matrix A?
  • · Replies 11 ·
Replies
11
Views
2K
High School Is it invalid to redefine the sgn function in this way in a proof?
  • · Replies 15 ·
Replies
15
Views
5K