Eigenvalue:
The unique collection of scalars connected to the system of linear equations.
It is also possible to refer to this concept as a characteristic value, characteristic root, appropriate value, or hidden root.
An input scalar that transforms the eigenvector.
The basic equation is Ax = λx
The number or scalar value “λ” is an eigenvalue of A.
Eigenvector:
Non-zero vectors that remain in their original direction after applying any linear transformation.
It only modifies by a single scalar factor.
In a summary, we may state that if x is a vector in vector space V that is not zero and A
is a linear transformation from V, then v is an eigenvector of A if A(X) is a scalar multiple of x.
An Eigenspace of vector x consists of a set of all eigenvectors with the equivalent eigenvalue collectively with
the zero vector.
Though, the zero vector is not an eigenvector.
Let us say A is an “n × n” matrix and λ is an eigenvalue of matrix A, then x, a non-zero vector,
is called as eigenvector if it satisfies the given below expression; Ax = λx
x is an eigenvector of A corresponding to eigenvalue, λ.
