Overview
Calculus
Computing Systems
Data
Graphs
Linear Algebra
Models and Modeling
Organization
Probability
Programming Constructs
- Programming Constructs Overview
- Abstraction
- Array
- Attribute
- Best-first Search
- Binary Search
- Block
- Branch
- Callback
- Class
- Conditional
- Constructor
- Container/Collection
- Dynamic Array
- Encapsulation
- Exception
- Expression
- Function
- Garbage Collection
- Greedy Algorithms
- Hash
- HTTP Request
- Identifier
- Inheritance
- Inner Class
- Instance
- Iterator
- Keyword
- Lambda
- Libraries
- List
- Linked List
- Literal
- Metaclass
- Method
- Mixin
- Object
- Operator
- Overloading
- Overriding
- Package
- Parameter
- Polymorphism
- Primitive
- Programming Process
- Recursion
- Reflection
- Regular Expression
- Reserved Word
- Return
- Sort
- Statement
- Switch
- Table
- This/Self
- Token
- Type
- Variable
Statistics
Trigonometry

Glossary and Index
Mathematical Symbols
Applications
Search
Blog
About the Author
Contact

Menu

The Science of Machine Learning & AI

Mathematics - Data Science - Computer Science

Overview
Calculus
Computing Systems
Data
Graphs
Linear Algebra
Models and Modeling
Organization
Probability
Programming Constructs
- Programming Constructs Overview
- Abstraction
- Array
- Attribute
- Best-first Search
- Binary Search
- Block
- Branch
- Callback
- Class
- Conditional
- Constructor
- Container/Collection
- Dynamic Array
- Encapsulation
- Exception
- Expression
- Function
- Garbage Collection
- Greedy Algorithms
- Hash
- HTTP Request
- Identifier
- Inheritance
- Inner Class
- Instance
- Iterator
- Keyword
- Lambda
- Libraries
- List
- Linked List
- Literal
- Metaclass
- Method
- Mixin
- Object
- Operator
- Overloading
- Overriding
- Package
- Parameter
- Polymorphism
- Primitive
- Programming Process
- Recursion
- Reflection
- Regular Expression
- Reserved Word
- Return
- Sort
- Statement
- Switch
- Table
- This/Self
- Token
- Type
- Variable
Statistics
Trigonometry

Glossary and Index
Mathematical Symbols
Applications
Search
Blog
About the Author
Contact

Mathematical Notation Powered by CodeCogs

This work is licensed under a Creative Commons Attribution 4.0 International License.

Blog RSS

Concatenation

Concatenation is the appending of vectors or matrices to form a new vector or matrix.

Vector concatenation can be applied as single row matrices.

As shown below, concatenation can be applied vertically, horizontally, or merged:

$\\M_{1}=\begin{bmatrix}1 &2 \\ 3 &4 \end{bmatrix} \\\\M_{2}=\begin{bmatrix}5 &6 \\ 7 &8 \end{bmatrix} \\\\C_{h}\left ( M_{1} ,M_{2}\right )=\begin{bmatrix} \begin{bmatrix}1 &2 \\ 3 &4 \end{bmatrix}, & \begin{bmatrix}5 &6 \\ 7 &8 \end{bmatrix}\end{bmatrix} \\\\C_{v}\left ( M_{1} ,M_{2}\right )=\begin{bmatrix} \begin{bmatrix}1 &2 \\ 3 &4 \end{bmatrix},\\\\ \begin{bmatrix}5 &6 \\ 7 &8\end{bmatrix}\end{bmatrix} \\\\C_{m}\left ( M_{1} ,M_{2}\right )=\begin{bmatrix}1 &2 & 3 &4 &5 & 6 & 7 & 8\end{bmatrix} \\\\\mathrm{\textup{where:}} \\\\M\,\,\,\,\mathrm{\textup{matrix}} \\C\,\,\,\,\,\,\mathrm{\textup{concatenation function}} \\h\,\,\,\,\,\,\,\mathrm{\textup{horizontal concatenation}} \\v\,\,\,\,\,\,\,\mathrm{\textup{vertical concatenation}} \\m\,\,\,\,\,\mathrm{\textup{merged concatenation}}$

References

Python NumPy Concatenate Function
Web Search
YouTube Search