Explore fiber symmetrization in the space of matrices through this 27-minute lecture by Julian Haddad at the Hausdorff Center for Mathematics. Delve into the process defined by Bianchi, Gardner, and Gronch that generalizes Steiner symmetrization to higher dimensions, replacing one-dimensional lines with m-dimensional subspaces. Examine its application in the space of n * m real matrices and discover interesting properties related to matrix multiplication. Review these properties and learn how they can be used to prove isoperimetric inequalities for convex bodies in matrix space.