An eigenvalue is a special number associated with a square matrix in linear algebra. When a matrix acts on a vector, the eigenvalue indicates how much the vector is stretched or compressed. Specifically, if you multiply a matrix by an eigenvector, the result is the same as multiplying the eigenvector by its corresponding eigenvalue. In mathematical terms, if A is a matrix and v is an eigenvector, then the relationship can be expressed as Av = λv, where λ represents the eigenvalue. Eigenvalues are crucial in various applications, including physics, engineering, and data analysis, as they help in understanding the properties of linear transformations.