Eigenvalues can be classified into different categories based on their properties. One such classification is whether they are positive, negative, zero, or infinite. In this case, the correct answer is 4, which means that eigenvalues can be negative values. Let's explain this in detail below.

What are Eigenvalues?
Eigenvalues are a fundamental concept in linear algebra that are associated with linear transformations or matrices. They represent scalar values that are derived from these transformations or matrices.

Properties of Eigenvalues:
Eigenvalues possess several properties, and one of them is their sign. They can be positive, negative, zero, or even infinite. Let's discuss each of these properties in detail.

1. Positive Eigenvalues:
Positive eigenvalues occur when all the eigenvalues of a matrix or transformation are positive real numbers. This means that the matrix or transformation stretches or expands the corresponding eigenvectors. Positive eigenvalues are often associated with growth or expansion in various mathematical and scientific applications.

2. Negative Eigenvalues:
Negative eigenvalues occur when all the eigenvalues of a matrix or transformation are negative real numbers. In this case, the matrix or transformation compresses or contracts the corresponding eigenvectors. Negative eigenvalues are often associated with decay or contraction in various mathematical and scientific applications.

3. Zero Eigenvalues:
Zero eigenvalues occur when at least one eigenvalue of a matrix or transformation is zero. This implies that the matrix or transformation collapses or flattens the corresponding eigenvectors to a single point or line. Zero eigenvalues are often associated with degeneracy or singularity in various mathematical and scientific applications.

4. Infinite Eigenvalues:
Infinite eigenvalues occur when at least one eigenvalue of a matrix or transformation is infinite. This indicates that the matrix or transformation stretches or expands the corresponding eigenvectors infinitely. Infinite eigenvalues are relatively less common and may arise in specific mathematical and scientific contexts.

Conclusion:
Eigenvalues can have various properties, including positive, negative, zero, or infinite values. The correct answer to the given question is 4, which states that eigenvalues can be negative values. It is important to consider the specific context and properties of the matrix or transformation to determine the sign of the eigenvalues and their implications in different applications.