Eigenvectors and eigenvalues are the two main concepts of Linear algebra.

Eigenvectors are unit vectors that have a magnitude equal to 1.0.

Eigenvalues are the coefficients that are applied to the eigenvectors, or these are the magnitude by which the eigenvector is scaled.

In the context of linear algebra and machine learning, eigenvalues and eigenvectors are essential concepts.

Eigenvalues (λ) are scalar values that represent how a linear transformation, represented by a square matrix, stretches or compresses a vector. They are often denoted as λ and can be calculated by solving the characteristic equation of the matrix.

Eigenvectors (v) are non-zero vectors that are unchanged in direction by a linear transformation, but may be scaled by a factor, which is the corresponding eigenvalue. In other words, when a matrix is applied to its eigenvector, the resulting vector is parallel to the original eigenvector.

To summarize:

Eigenvalues represent the scale at which the eigenvectors are stretched or compressed.
Eigenvectors represent the directions that remain unchanged under the transformation.

In the context of artificial intelligence interviews, it’s crucial to understand these concepts as they have applications in various areas such as principal component analysis (PCA), feature extraction, solving differential equations, and understanding the behavior of iterative algorithms like PageRank in web search algorithms.