Verify Eigenvector

Implement a function to verify if a given vector is an eigenvector of a matrix with a specified eigenvalue. This concept is crucial in linear algebra as eigenvectors represent directions in which a matrix transformation scales a vector by a factor, known as the eigenvalue. The equation $A\mathbf{v} = \lambda\mathbf{v}$ represents this relationship, where $A$ is the matrix, $\mathbf{v}$ is the eigenvector, and $\lambda$ is the eigenvalue.

To verify if $\mathbf{v}$ is an eigenvector of $A$ with eigenvalue $\lambda$, we need to check if the matrix $A$ transforms $\mathbf{v}$ into a scaled version of itself. Here are the steps:

1. Compute the product of $A$ and $\mathbf{v}$.
2. Compute the product of $\lambda$ and $\mathbf{v}$.
3. Compare the results to determine if they are equal.

This technique is widely used in computer vision for image compression and dimensionality reduction.