State the definition of an eignenvalue and eigenvectorSoluti

State the definition of an eignenvalue and eigenvector.

Solution

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, characteristic values.

Eigenvectors are a special set of vectors associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic vectors, proper vectors, or latent vectors.

For example, A scalar is called an eigenvalue of the n × n matrix A is there is a nontrivial solution x of Ax = x. Such an x is called aneigenvector corresponding to the eigenvalue .