Field Theory Concept & Examples -

Running head: Math 220
Math 220
Name of the Student
Name of the University

Math 220 2

Math 220 3
Introduction:
1.
Linear Algebra is a field of mathematics that deals with linear functions and their
representations in vector spaces often with the aid of matrices. This has many real life
application some of which will be discussed in this report.
Some of the applications of linear algebra in our contemporary world is ranking search
engine, error correcting codes, graphics, signal analysis, linear programming, community
detection, quantum computing and others.
In this report the mathematic behind linear programming will be studied which uses a
method from linear algebra called the Gaussian elimination method. In fact the simplex
method in linear algebra is a just a sophisticated expansion of the Gaussian elimination
method.
The algorithm Gaussian elimination method is mainly used to solve systems of linear
equations. It is in reality a sequence of operations performed on the corresponding matrix of
coefficients. This method is often used to find the determinant of matrix to calculate the
inverse of an invertible matrix. This method was named after a German mathematician Carl
Friedrich Gauss who is thought to be the first person to have discovered the method.
2.
The range of application of this short but simple method is vast. Here we will briefly touch on
a few topics.
Gauss elimination method is used in enhancing image. The technique used for this is called
“Directional Gaussian Filter”. Image filtering such as fingerprint image and non-subsample
countour transform process is applied along with other techniques to attain good images from
thumb impressions.