Courses

Get the App

Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev

GATE Computer Science Engineering(CSE) 2022 Mock Test Series

Computer Science Engineering (CSE) : Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev

The document Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev is a part of the Computer Science Engineering (CSE) Course GATE Computer Science Engineering(CSE) 2022 Mock Test Series.

All you need of Computer Science Engineering (CSE) at this link: Computer Science Engineering (CSE)

Eigen Values and Eigen Vectors

Eigen vector of a matrix A is a vector represented by a matrix X such that when X is multiplied with matrix A, then the direction of the resultant matrix remains same as vector X.

Mathematically, above statement can be represented as:

AX = λX

where A is any arbitrary matrix, λ are eigen values and X is an eigen vector corresponding to each eigen value.

Here, we can see that AX is parallel to X. So, X is an eigen vector.

Method to find eigen vectors and eigen values of any square matrix A

We know that,

AX = λX

=> AX – λX = 0

=> (A – λI) X = 0 …..(1)

Above condition will be true only if (A – λI) is singular. That means,

|A – λI| = 0 …..(2)

(2) is known as characteristic equation of the matrix.

The roots of the characteristic equation are the eigen values of the matrix A.

Now, to find the eigen vectors, we simply put each eigen value into (1) and solve it by Gaussian elimination, that is, convert the augmented matrix (A – λI) = 0 to row echelon form and solve the linear system of equations thus obtained.

Some important properties of eigen values

Eigen values of real symmetric and hermitian matrices are real
Eigen values of real skew symmetric and skew hermitian matrices are either pure imaginary or zero
Eigen values of unitary and orthogonal matrices are of unit modulus |λ| = 1
If λ_1,λ₂…….λ_n are the eigen values of A, then kλ₁, kλ₂…….kλ_n are eigen values of kA
If λ_1,λ₂…….λ_n are the eigen values of A, then 1/λ₁, 1/λ₂…….1/λ_n are eigen values of A^-1
If λ_1,λ₂…….λ_n are the eigen values of A, then λ₁^k, λ₂^k…….λ_n^k are eigen values of A^k
Eigen values of A = Eigen Values of A^T(Transpose)
Sum of Eigen Values = Trace of A (Sum of diagonal elements of A)
Product of Eigen Values = |A|
Maximum number of distinct eigen values of A = Size of A
If A and B are two matrices of same order then, Eigen values of AB = Eigen values of BA

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Download EduRev app here for Computer Science Engineering (CSE) preparation.

Up next

Author

Gate Gurus

Views

5.1K

Rating

4.8

Description

Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev notes for Computer Science Engineering (CSE) is made by best teachers who have written some of the best books of Computer Science Engineering (CSE). It has gotten 5117 views and also has 4.8 rating. You can download Free Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev pdf from EduRev by using search above. You can also find Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev ppt and other Computer Science Engineering (CSE) slides as well. If you want Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev Tests & Videos, you can search for the same too. Computer Science Engineering (CSE) Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev Summary and Exercise are very important for perfect preparation. You can see some Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev sample questions with examples at the bottom of this page. Complete Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev chapter (including extra questions, long questions, short questions, mcq) can be found on EduRev, you can check out Computer Science Engineering (CSE) lecture & lessons summary in the same course for Computer Science Engineering (CSE) Syllabus. EduRev is like a wikipedia just for education and the Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev images and diagram are even better than Byjus! Do check out the sample questions of Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev for Computer Science Engineering (CSE), the answers and examples explain the meaning of chapter in the best manner. This is your solution of Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev search giving you solved answers for the same. To Study Eigenvalues and Eigenvectors Computer Science Engineering (CSE) Notes | EduRev for Computer Science Engineering (CSE) this is your one stop solution.

GATE Computer Science Engineering(CSE) 2022 Mock Test Series

131 docs|167 tests

Up next

Matrices

Viva Questions

practice quizzes

ppt

pdf

Objective type Questions