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  Linear Algebra in MATLAB

Linear algebra:

Linear algebra is the branch of mathematics. It is about vector spaces, often finite or countable infinite dimensional, plus linear mappings among such spaces. Linear algebra is essential to both applied and pure mathematics. For example, abstract algebra occurs by relaxing the axioms of a vector space. Linear equations are logically represented by using the formalism of vectors and matrices.

The main objective of this topic is to become people familiar with the concept of using a MATLAB to perform linear algebra. MATLAB is a program which performs linear algebra very well, and it is very frequently used by mathematicians, engineers and scientists etc. It helps to solve problems that could be impractical to answer by hand.

We can number of operations in linear algebra like analysis of matrix, linear equations, singular values, logarithms, factorization, exponentials etc. The MATLAB library contains more than 40 functions for linear algebra such as info(linalg).

Library 'linalg': the linear algebra package:

 -- Interface:

linalg::basis,            linalg::charmat,
linalg::addCol,           linalg::addRow,
linalg::adjoint,          linalg::angle, etc.

After exported, library functions could be used by their short notation. The function call use(linalg) exports all functions of linalg. After exporting this function one can use the the other functions by their short form like name gaussElim can be used instead of linalg::gaussElim.

The simple way to describe a matrix A is using the command matrix. The syntax of defining a 2 ? 2 matrix is as follows:

A := matrix ([[1, 2], [3, 2]])

1638_matrix.jpg

Now after defining matrices we can perform different operations like multiplication, inverse, Exponential of matrices, adjoint and transpose of matrix etc.

Various processes from linear algebra are as well used in analytic geometry, engineering, physics, computer science, computer animation, and in economics. Because linear algebra is such a well-managed theory, nonlinear mathematical models are occasionally estimated by linear ones. We can plot complex functions by plotting commands with functions of a complex variable. By using MATLAB we can define different complex numbers in linear algebra like, Cartesian form, polar form, arithmetic with complex form, complex conjugate, real and imaginary, modulus and angle etc.

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