Computing in Scilab

Introduction

Matrices are often aptly described as key to solve everything in the scientific world. This chapter expounds the usefulness of vectors and matrices that occur in many kinds of problems across the disciplines. They are used to study innumerable physical phenomena such as, motion of rigid bodies, eigen states of a quantum mechanical system, electrical networks and coordinate system conversion.

In Scilab, matrix computation forms the basis of all calculations. This chapter recapitulates the basic Scilab rules that have to be followed for creating and editing matrices. It also summarizes the arithmetic operations that can be performed on matrices. Section 1.2 gives an overview on different ways of generating a matrix and its elements. Some special types of matrices such as row/column vector, diagonal matrix, identity matrix and triangular matrices have been introduced in Section 1.3. Matrix operations such as row/column operation, conjugation, scalar/vector multiplication and division have been explained in Section 1.4. The laws of vector algebra have been outlined in Section 1.5. Some interesting examples of applications and use of matrices in physical sciences have been discussed in Section 1.6.

Creation of a Matrix

Matrices are rectangular arrangements of ‘m’ rows and ‘n’ columns; an arrangement of m rows and n columns is called an (m × n) matrix. If it contains only one row or only one column, then it is called a vector. There are several ways of defining vectors and matrices in Scilab. Some of them have been explained as follows.

• 1. The elements of a matrix are defined by writing them inside a square bracket, such that the elements of a row are separated by a comma or a white space. The elements of consecutive rows are separated by a semi-colon.

• 2. The elements of a matrix can be of several types and have been listed in Table 1.1. As can be seen in this table,

  • a. The elements can be real numbers.

  • b. The elements can be complex numbers. The complex number consists of a real part and/or an imaginary part.

  • c. The elements can be rational numbers, which are defined using the ‘rlist’ command of Scilab.