Can a non-square matrix have eigenvalues? 

No, a non-square matrix cannot have eigenvalues. 

Eigenvalues are defined only for square matrices. This is because the eigenvalue equation \( \mathbf{A}\mathbf{v} = \lambda \mathbf{v} \) requires the matrix \(\mathbf{A}\) to be square so that \(\mathbf{v}\), the eigenvector, and \(\lambda\), the eigenvalue, are well-defined. In other words, eigenvalues are the roots of the characteristic equation, which is derived from the determinant of the matrix subtracted by \(\lambda\) times the identity matrix, and determinants are defined only for square matrices.

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Here are 5 related questions:
1. What is the characteristic equation of a matrix?
2. How do you calculate the eigenvalues of a square matrix?
3. What are some applications of eigenvalues in various fields?
4. Can a rectangular matrix be converted to a square matrix to find eigenvalues?
5. How do eigenvectors relate to eigenvalues?

**Tip:** In practice, even though non-square matrices don't have eigenvalues, they can have singular values, which are related to the concept of eigenvalues and are used in Singular Value Decomposition (SVD).

Explore why non-square matrices cannot have eigenvalues and the fundamental concepts of eigenvalues in linear algebra. This article covers the eigenvalue equation, characteristic equation, and theorems related to eigenvalues in square matrices. Suitable for advanced high school and college-level students.

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