Question

Explain eigan value as well as write its expression ?​

Answer 1

Answer:

Definition of eigenvalue:

a scalar associated with a given linear transformation of a vector space and having the property that there is some nonzero vector which when multiplied by the scalar is equal to the vector obtained by letting the transformation operate on the vector especially : a root of the characteristic equation of a matrix

Eigenvectors

An eigenvector of a square matrix A is a nonzero vector x such that for some number λ, we have the following:

Ax = λx

We call λ an eigenvalue.

So, in our example in the introduction, λ = 3,

X=[2

3

4]

Notice that if x = cy, where c is some number, then

A(cy) = λcy

cAy = λcy

Ay = λy

Therefore, every constant multiple of an eigenvector is an eigenvector, meaning there are an infinite number of eigenvectors, while, as we'll find out later, there are a finite amount of eigenvalues. Each eigenvalue will have its own set of eigenvectors.

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Answer 2

Suppose A be the sequare matrix of order n by n then a number (real or complex) lamda is said to be eigan value of matrix of x of order n by 1 such that

Ax= lamda *x

Lamda called eigan value of A

X called eigan vactor of A