Frobenius was a student of Weierstrass. Landau & Schur were two of his top students. Without him, the familiar matrices of linear algebra would never had taken the form we know today. Although less emphasized by pedagogy than other matrix decompositions such as spectral/eigenvalue, singular value, the Schur decomposition is closely related to the QR decomposition. The Golub-Kahan variant is perhaps the most important LAPACK subroutine (DBDSQR):
https://www.netlib.org/lapack/double/dbdsqr.f