This is something that I haven't really found much info on. I'm a student attending McGill university, and I have a choice between taking Honours Applied Linear Algebra and Honours Algebra. Linear algebra: Mathematics & Statistics (Sci) : Matrix algebra, determinants, systems of linear equations. Abstract vector spaces, inner product spaces, Fourier series. Linear transformations and their matrix representations. Eigenvalues and eigenvectors, diagonalizable and defective matrices, positive definite and semidefinite matrices. Quadratic and Hermitian forms, generalized eigenvalue problems, simultaneous reduction of quadratic forms. Applications. Algebra: Mathematics & Statistics (Sci) : Linear equations over a field. Introduction to vector spaces. Linear maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and quadratic forms. Real and complex inner product spaces. Diagonalization of self-adjoint operators. Now, generally the physicists take the linear algebra while the mathematicians take algebra. I'm interested in theoretical physics (currently GR, string theory, and astro), but since I'm only second year that may change.