It is true that Finding an eigenvector of A may be difficult, but checking whether a given vector is in fact an eigenvector is easy.
A square matrix's eigenvector is described as a non-vector that, upon multiplication, becomes a scalar multiple of the supplied matrix.
Let's assume that A is a n x n square matrix, and if v is a non-zero vector, then the product of matrix A, vector v, and the given vector is defined as the product of the scalar quantity and the supplied vector, such that:
Av =λv
Where , v = Eigenvector and let be the scalar quantity referred to as the eigenvalue for the specified matrix A.
To find eigenvectors , we have to find eigen values but to check if they are eigenvectors All we have to do is to check if its satisfy the equation of matrix
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