Yes, a matrix can have more than one eigenvalue. An eigenvalue is a scalar that represents a specific characteristic of the matrix. It can be thought of as a scaling factor applied to the eigenvector.

  For example, consider a 2x2 matrix:

  A = [2 0]

   [0 3]

  In this case, the matrix has two distinct eigenvalues, λ₁ = 2 and λ₂ = 3. The corresponding eigenvectors are v₁ = [1 0]ᵀ and v₂ = [0 1]ᵀ, respectively.

  Eigenvalues and their corresponding eigenvectors play a crucial role in many applications, such as eigenvalue decompositions, diagonalization, and solving systems of linear differential equations. It is common for matrices to have multiple eigenvalues, each associated with its eigenvector.