# Get the Knowledge that sets you free...Science and Math for K8 to K12 students

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## Matrices

Matrices in computer applications One of the most important usages of matrices in computer side applications are encryption of message codes. Matrices and their inverse matrices are used for a programmer for coding or encrypting a message. A message is made as a sequence of numbers in a binary format for communication and it follows code theory for solving. Hence with the help of matrices, those equations are solved. With these encryptions only, internet functions are working and even banks could work with transmission of sensitive and private data.

## Introduction

A rectangular arrangement of numbers in the form of horizontal and vertical lines is called a matrix (plural form: "matrices"). The horizontal lines are called rows and the vertical lines are called columns of a matrix. Numbers that appear in the rows and columns of a matrix are called its elements or its entries. The elements are together enclosed in a brackets [ ] or parentheses ( ). The arrangement of numbers below is an example of a matrix.

The number of rows and columns that a matrix has is called its dimension or its order. By convention, rows are listed first and columns, second. Thus, we would say that the dimension (or order) of the above matrix is 3 × 3 (read "3 by 3"), meaning that it has 3 rows and 3 columns. In the above matrix, 11, 22, 33, 12, 24, 36, 10, 20 and 30 are called its elements.

Matrices in robotics and automation In robotics and automation, matrices are the base elements for the robot movements. The movements of the robots are programmed with the calculation of rows and columns of matrices. The inputs for controlling robots are given based on the calculations from matrices.
Matrix Notation

A matrix is usually represented by an upper–case letter (such as A, B, C, or D), while the corresponding lower–case letter, with two subscript indices (eg: a11, b11, c11), represent the elements.

In the matrix , a11 represents the element in the first row and first column, a12 represents the element in the first row and second column, a21 represents the element in the second row and first column, and a22 represents the element in the second row and second column.

General form of a matrix: In general, a set of 'mn' elements can be arranged as a matrix having 'm' rows and 'n' columns as below:

In the above matrix aij represents an element of the matrix A occurring in ith row and jth column. The maximum value of 'i' can be 'm' ie. number of rows and the maximum value of 'j' can be 'n' ie. number of columns.

Use of square matrices in DNA Profiling In DNA Profiling, analyzing DNA sequences and mapping the genes can be made possible by square matrices. With the help of this phenomenon, the similarities and dissimilarities of genes are recorded in rows and columns. These square matrices are extensively used in DNA identification in multiple–fatality cases.
Square Matrix

A matrix in which number of rows is equal to number of columns is called a square matrix. Thus, an m × n matrix for which m = n is called a square matrix of order ‘n’. In the below figure, the matrices A and B are square matrices of order 3 and 2 respectively.

The elements aij of a square matrix A = [aij]n × n for which i = j, that is, the elements a11, a22, a33, ...., ann are called the diagonal elements and the line along which they lie is called the principal diagonal of the matrix. In the above figure, the elements 1, 5, 9 constitute the principal diagonal of the matrix A and the elements 2, 7 constitute the principal diagonal of the matrix B.