# What are the uses of Eigen Values and Eigen Vectors? # Introduction

What are the uses of Eigen Values and Eigen Vectors? In this paper we will know about the various examples of the values ​​of eigen and eigen vectors. Eigen prices and eigen vectors have found their various uses in the communication system, Bridge Construction, Automobile Stereo system design, Electrical Engineering, Mechanical Engineering. Oil companies are often used to explore the world for oil.

Here we will consider the app to explain how it works.

## Eigen value:

Let A = [aij] nxn be the aquare matrix of order n over field F. The element LEMBDA in F is called, the value of the element A if

= 0 when I am an order matrix unit n.

## Eigen Vector:

LAMBDA must be the eigen value of the square n matrix n of the scheme nx1 (i.e. column matrix) so that (A-XI) X = 0 be the eigen vector of A corresponding to the value of eigen LAMBDA.

### REAL EXAMPLE OF EIGEN VALUE AND EIGEN VECTORS:

The vector that enters the pure scale without rotation is known as the eigen vector

The measuring factor is called the eigen value.

NOTE: If eigen values ​​and eigen vectors are considered or complex then any input vectors will be rounded to a certain value.

### Understanding scale and no rotation:

Take the cylindrical objects and draw two vectors x1 and x2 on them. The X1 is an axis line to the cylinder and the x2 is 45 degrees. We will try to understand what happens after performing ax1 and ax2 surgery. Now matrix A will appear in my church action. So after twisting the object closely look at x1 and x2 and see what we get so notice the x1 at first so that it starts horizontally now it is rotated and measured try to see it and do the same thing with x2 focus on x2. It just seems to weigh but not rotate. We can also twist the other way into the same thing that happens to measure but there is no rotation which is why in our understanding we know that x2 is an eigen vector and x1 is not. Let’s see where this concept is applied to real-world applications, the distortions we have seen typically occur in your nature or in the modification of car driving in some way. The eigen value problem is used to design these components.

Statistically:

A = 1 2 X = 1

2 4 1

AX = 3

6

Measured and rotated

Case 2:

A = 1 2 X = 1

2 42

Measure but not rotated

SECOND USE OF EIGEN VALUES AND EIGEN VECTORS:

### Applications of Linear Algebra in Electrical Engineering

The values ​​of eigen and eigen vectors play a major role in the field of electrical engineering. We use a symmetrical component modification to terminate a beneficial three-phase system. We can also determine the cause of the open and short circuit. In an open circuit, there is no conductivity while the infinite conductivity between the nodes indicates an open circuit.

THIRD PERFORMANCE OF EIGEN VALUE AND EIGEN VECTORS:

### Fibonacci Series:

0 1 1 2 3 5 8 13 21 34 55 89 144 233 ……………………………

Fn = F (n-1) + F (n-2)

The third term is the sum of the last two terms. Now we want to know the next number using the multiplicand matrix.

Fn = 1 1 x F (n-1)

F (n-1) 1 0 F (n-2)

It also integrates computer algorithms such as the Fibonacci search method and the Fibonacci bulk data structure and graph called Fibonacci cubes used to connect compatible and distributed systems.

### Conclusion:

If we want to reduce the performance of the line to a simple problem and divide it then the values ​​of eigen and eigen vectors are very helpful. Examples: plastic and any solid and dense material can become damaged if we put pressure or pressure on it. They can receive basic guidance. Moreover the deformation is very large in those methods.