Matrices

 

Introduction to Matrices

    Matrix applications are widely used in mathematics as well as other subjects. It aids in the solution of linear equations. Matrices are incredibly valuable items that can be found in a variety of settings. The usage of matrices in mathematics can be found in a wide range of scientific and mathematical subjects. Almost every element of our life is influenced by engineering mathematics. In this post, we'll go over what a matrix is, how to use matrices, and how to solve problems using matrices.

    They are used in computer graphics to project a three-dimensional image onto a two-dimensional screen. Stochastic matrices are used to explain sets of probabilities in probability theory and statistics; for example, they are utilised in the page rank algorithm that ranks the sites in a Google search.

What are Matrices?

• A matrix is defined as a rectangular array of numbers or symbols which are generally arranged in rows and columns.

• The order of the matrix can be defined as the number of rows and columns.

• The entries are the numbers in the matrix known as an element.

• The plural of a matrix is matrices.

• The size of a matrix is denoted as ‘n by m’ matrix and is written as m×n, where n = number of rows and m = number of columns.

Types of Matrix

There are different types of matrices. Here they are:

1) Row matrix

2) Column matrix

3) Null matrix

4) Square matrix

5) Diagonal matrix

6) Upper triangular matrix

7) Lower triangular matrix

8) Symmetric matrix

9) Anti-symmetric matrix

 

Applications of Matrices

Matrices have many applications in diverse fields of science, commerce and social science. Matrices are used in:

(i) Computer Graphics 

(ii) Optics 

(iii) Cryptography 

(iv) Economics

(v) Chemistry 

(vi) Geology 

(vii) Robotics and animation 

(viii) Wireless communication and signal processing 

(ix) Finance ices

(x) Mathematics

 

Use of Matrices in Computer Graphics

Earlier, architecture, cartoons, and automation were done by hand drawings but nowadays they are done by using computer graphics. Square matrices very easily represent the linear transformation of objects. They are used to project three-dimensional images into two-dimensional planes in the field of graphics. In graphics, a digital image is treated as a matrix to start with. The rows and columns of the matrix correspond to rows and columns of pixels and the numerical entries correspond to the pixels’ colour values.

Using matrices to manipulate a point is a common mathematical approach in video game graphics. Matrices are also used to express graphs. Every graph can be represented as a matrix, each column and each row of a matrix is a node and the value of their intersection is the strength of the connection between them. Matrix operations such as translation, rotation and sealing are used in graphics.