Row Matrix

A matrix is a rectangular arrangement of numbers organized in rows and columns. The size of a matrix is described by the number of rows and columns present in it. A matrix with m rows and n columns is said to be of order m × n. A row matrix has only one row but can have any number of columns. Its order is represented as 1 × n. All of its elements are aligned horizontally in this single row.
 

The order of a row matrix is written as 1 × n, meaning it has 1 row and n columns, where n can be any positive number. 

Transpose of a Row Matrix

While taking the transpose of a row matrix, we turn its single horizontal row into a vertical column. So, a matrix with 1 row and n columns becomes a matrix with n rows and 1 column. This new matrix is called the transpose, and it's written as A’ or AT.
For example, if A = [2 4 6], which is a 1 × 3 row matrix, then its transpose is At:

Properties of Row Matrix 

Listed below are the properties of a row matrix:

1. Row matrices only have one row.
2. In a row matrix, the number of elements is the same as the number of columns, since all the entries are arranged in a single row.
3. Row matrices are rectangular matrices.
4. The transpose of a row matrix 1 × n is a column matrix n × 1.
5. Row matrices can be added or subtracted only if they have the same number of columns (i.e., the same order).
6. A row matrix can be multiplied by its transpose to produce a square matrix.
7. Multiplying a row matrix by a compatible column matrix results in a 1×1 matrix, also known as a scalar or singleton matrix.
    

Row matrices differ from column matrices in the following aspects:
 

Two primary operations that can be performed on a row matrix are addition and subtraction. Let’s learn how they are executed in detail.

Addition of row matrices

Two matrices can be added together only if they are both of the same order. In this case, the sum is obtained by adding each pair of matching elements. For example,
Let A = [3 5 7] and
B = [1 2 4]
Both matrices are of order 1 × 3, so they can be added.
A + B = [3 5 7] + [1 2 4] 
= [(3 + 1) (5 + 2) (7 + 4)]
= [4 7 11]

Subtraction of row matrices

Similar to addition, two row matrices can be subtracted only if they are of the same order and the operation involves subtracting corresponding entries. For example,
Let A = [8 6 4], and
B = [3 2 1]
Both these matrices are of the same order, i.e., 1 × 3, so they can be subtracted.
A - B = [8 6 4] - [3 2 1]
= [(8 - 3) (6 - 2) (4 - 1)]
= [5 4 3]
 

Row matrices have many real-life applications in various fields. Some of them have been listed below: 

• Storing exam scores 
  Student marks across different subjects can be organized as a row matrix for easier analysis. For example, if a student scores 10 in Math, 15 in Science, 18 in English, and 11 in History, the marks can be written as:
  Marks = [10, 15, 18, 11]
  This 1 × 4 matrix format helps quickly compare scores across subjects or calculate averages.
  
   
• RGB color representation in graphics
  The colors red, green, and blue can be represented as a row matrix in computer graphics and used in image processing. Each pixel color is a row matrix of RGB values.
  
   
• Representing preferences in recommendation systems
  In platforms like Netflix, a user’s movie preferences can be represented as a row matrix, where each column shows interest levels in different genres.
  For example, a row matrix like [5 3 0 4] might represent a user's ratings for ‘horror,’ ‘comedy,’ ‘romance,’ and ‘action,’ respectively.
  This kind of structure makes it easier for machine learning models to compare users and suggest similar content.
  
   
• Sensor readings on devices
  In IoT and robotics, readings from multiple sensors at a single point in time can be stored as a row matrix. For example, Readings = [30.4  60  1214.2  5.3] (Temp, Humidity, Pressure, Speed)
  
   
• Representing the distance from one city to another
  In travel or logistics planning, a row matrix can be used to show the distances from one central city to several others.
  For example, if city A is connected to cities B, C, and D, the distances can be stored as: Distances = [120, 200, 95]
  This 1 × 3 row matrix helps in comparing routes quickly, calculating travel times, or optimizing delivery paths.