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1. EIGENVALUES AND EIGENVECTORS
Department Of Computer Science Engineering
Submitted By:
Gourav Kumar Nath (MT/CS/10001/24)
Shahbaz Alam (MT/CS/10013/24)
Gaurav Kumar (MT/CS/10015/24)

2. Eigenvalues and Eigenvectors
The vector x is an eigenvector of matrix A and λ is an
eigenvalue of A if: Ax= λx
Eigenvalues and eigenvectors are only defined for square
matrices.
Eigenvectors are not unique.
Zero vector is a trivial solution to the eigenvalue equation
for any number λ and is not considered as an eigenvector.

3. APPLICATION OF EIGEN VALUE AND EIGEN VECTOR
Network Connectivity and Stability
Network connectivity and stability are critical concepts in analyzing how well-
connected and resilient a network is to potential failures. Eigenvalues and
eigenvectors are widely used in this context, particularly through
 
graph
theory 
and 
Laplacian matrices.
A is An n×n Adjacency Matrix.
Constructing the Laplacian Matrix

4. Eigenvalues of the Laplacian
Matrix

5. THANK YOU