MATLABit
MATLAB, short for MATrix LABoratory, is a powerful programming language and integrated software environment developed by MathWorks. It is widely used in engineering, scientific research, academic instruction, and algorithm development because of its strengths in numerical computation, data analysis, graphical visualization, and simulation. Built on matrix algebra, MATLAB efficiently handles large datasets and complex calculations. In this guide, we will focus on creating matrices in MATLAB. Matrices are a fundamental concept in MATLAB, used for storing multi-dimensional data, performing calculations, and analyzing datasets. Beginners will learn how to define, initialize, and manipulate matrices, enabling them to work efficiently with MATLAB for both basic and advanced computations.
Table of Contents
- Introduction
- Significance
- Other Ways to Create Matrices
- Applications of Creating Matrices in MATLAB
- Conclusion
Introduction
Numbers are arranged in rows and columns forming a two-dimensional array, also known as a matrix. Matrices can be used to store information like a table. They describe a wide range of physical quantities in science and engineering and are crucial to linear algebra.
Square and Rectangular Matrices
The number of rows and columns in a square matrix are equal. For instance, the below given matrix is 4 × 4:
| t1 | t2 | t3 | t4 |
| t5 | t6 | t7 | t8 |
| t9 | t10 | t11 | t12 |
| t13 | t14 | t15 | t16 |
Size: 4 × 4
Also, for 5 × 4:
| 21 | 14 | 30 | 7 |
| 3 | 25 | 19 | 11 |
| 28 | 6 | 15 | 22 |
| 17 | 9 | 34 | 5 |
| 13 | 18 | 24 | 20 |
Size: 5 × 4
There are m rows and n columns in a m × n matrix. The matrix's size is "m by n."
Creating a Matrix (Row by Row)
By allocating the matrix's components to a variable, a matrix is produced. Insert each element a single at a time inside square brackets [ ]. Use commas or spaces to divide consecutive elements.
To start a new row, use a
semicolon (;) or press Enter. Close with the right bracket ].
variable_name = [elements in the first, second, and third rows;
... ; last row elements]
Example (4 × 4):
A = [t1 t2 t3 t4; t5 t6 t7 t8; t9 t10 t11 t12; t13 t14 t15 t16]Example (5 × 4):
B = [21 14 30 7; 3 25 19 11; 28 6 15 22; 17 9 34 5; 13 18 24 20]Significance
Creating matrices in MATLAB is a core concept that underpins almost all numerical computation and data analysis tasks performed in the environment. MATLAB is specifically designed for matrix-based operations, and its name itself reflects this focus. A matrix in MATLAB is a two-dimensional array of numbers arranged in rows and columns, and it is used to represent data, images, systems of equations, transformations, and many other mathematical structures. Understanding how to create matrices correctly is essential for students, engineers, and researchers who rely on MATLAB for problem solving.
The most basic way to create a matrix in MATLAB is by using square brackets. Elements within the same row are separated by spaces or commas, while semicolons are used to indicate the start of a new row. This method is intuitive and allows users to explicitly define each element of the matrix. It is particularly useful when working with small matrices or when the exact values are known beforehand. MATLAB automatically interprets the arrangement of numbers and stores them in a structured two-dimensional format.
MATLAB also provides several built-in functions to create matrices with specific characteristics. Functions such as zeros, ones, and eye are commonly used to generate matrices filled with zeros, ones, or identity values, respectively. These functions are especially important for initializing matrices before performing calculations. Preallocating matrices using these functions improves performance, particularly when dealing with large datasets or iterative algorithms, as it avoids the overhead of dynamically resizing arrays.
Another powerful method for creating matrices is by using the colon operator and related functions such as linspace and meshgrid. The colon operator can be used to generate row vectors that can later be reshaped into matrices. The linspace function creates evenly spaced values that are useful in numerical simulations and plotting. Functions like meshgrid are widely used in two-dimensional and three-dimensional computations, where matrices represent coordinate grids for surfaces and fields.
MATLAB also allows users to create matrices by combining or concatenating existing arrays. Horizontal and vertical concatenation enable the construction of larger matrices from smaller ones. This approach is useful when data is collected in segments or when building block matrices for advanced mathematical models. MATLAB ensures that dimensions are compatible during concatenation, helping users maintain logical and mathematical consistency.
Matrices can also be created by importing data from external sources such as text files, spreadsheets, or measurement devices. MATLAB provides functions to read data from files and store it directly into matrix form. This capability is essential for real-world applications where data is generated outside MATLAB. Once imported, the data can be processed, analyzed, and visualized using MATLAB’s extensive matrix operations.
Creating matrices efficiently in MATLAB also supports vectorized and matrix-based computations, which are faster and more readable than loop-based approaches. MATLAB is optimized to perform operations on entire matrices at once, making it possible to solve complex problems with concise code. By mastering matrix creation techniques, users can fully exploit MATLAB’s computational power and write clear, efficient, and professional programs.
In conclusion, creating matrices in MATLAB is a fundamental skill that enables effective numerical computation and data analysis. Whether matrices are defined manually, generated using built-in functions, formed through concatenation, or imported from external data, they provide a flexible and powerful structure for representing information. A strong understanding of matrix creation lays the foundation for advanced MATLAB programming, simulation, and research applications.
Other Ways to Create Matrices
Numbers or mathematical expressions comprising numbers, functions, and predefined variables can be entered as elements. Each row has to comprise the identical number of elements. Enter 0 if an element is zero. If you try to define an incomplete matrix, MATLAB will show you an error message.
MATLAB example:
> A = [5:2:15; 5:5:30; linspace(40,90,6); 5 4 3 7 8 0]
A =
5 7 9 11 13 15
5 10 15 20 25 30
40 50 60 70 80 90
5 4 3 7 8 0
>>
Examples of expressions in matrix elements
Matrix elements may be simple numbers or mathematical expressions. The expressions are evaluated when the matrix is created, so you can use arithmetic, variables, and MATLAB functions.
Arithmetic expressions:
> A = [3+1 2-9 4*5; 7^2 7+0 3-2]
A = 4 -7 20
49 7 1
Using variables:
> y = 5;
>> B = [y*3 2+y y^0; y-1 y y^2]
B =
15 7 1
4 5 25
Using functions and constants:
> C = [sqrt(16) sin(pi/2) cos(0); linspace(50,52,3)]
C =
4 1 1
50 51 52
Zeros and explicit entries:
> D = [2 1 2; 5 0 7]
D =
2 1 2
5 0 7
What causes an error:
> % Rows with different numbers of elements cause an error
>> E = [1 2 3; 4 5]
Error using <...>
Matrix dimensions must agree.
These examples show how flexible MATLAB is when building matrices: you can mix arithmetic, variables, and functions as long as each row has the same number of evaluated elements.
Applications of Creating Matrices in MATLAB
Matrices are used throughout scientific work and technology. Below are common application areas with short MATLAB-style examples to show how matrices appear in practice.
1. Solving linear systems
It is possible to reduce plenty of physical models to Lx = c systems of linear equations. MATLAB solves these efficiently with the backslash operator.
> L = [3 2; 1 4];
>> c = [5; 6];
>> x = L \ c; % solve Lx = c
2. 2D transformations and computer graphics
Rotations, scaling, and shearing are represented by matrices. A matrix multiply is the process of applying a transformation to a vector.
> theta = pi/6; % 30 degrees
>> T = [cos(theta) -sin(theta); sin(theta) cos(theta)];
>> vec = [1; 0];
>> R0 = T * vec; % rotated vector
3. Image processing
Digital images are matrices (grayscale) or 3D arrays (RGB). Matrix operations perform filtering, resizing, and color transforms.
> I = imread('coins.png'); % image stored as matrix/array
>> s = size(I);
>> J = imresize(I, 0.5); % resize using matrix interpolation
4. Engineering and physics
Matrices appear in finite-element models, state-space models for control systems, stress/strain tensors, and more.
These examples illustrate how matrices provide a compact, uniform way to represent and manipulate structured numerical data. Because MATLAB and similar environments are optimized for matrix operations, many algorithms are implemented by combining a few concise matrix commands.
Conclusion
Matrices are a fundamental way to organise numerical information into rows and columns. They can be square or rectangular (an m × n matrix has m rows and n columns), and their elements can be numbers or evaluated mathematical expressions, including variables and functions. MATLAB makes it easy to create and manipulate matrices using concise row-by-row notation, ranges, and built-in functions. Because many scientific, engineering, and data problems reduce to structured numerical operations, matrices—and efficient matrix operations—are central tools in computation and analysis.
