Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them (e.g. $$(x_1, \dots, x_n)\mapsto a_1x_1 + \dots + a_nx_n$$). Concepts include systems of linear equations, bases, dimensions, subspaces, matrices, determinants, kernels, null spaces, column spaces, traces, eigenvalues and eigenvectors, diagonalization, Jordan normal forms, and so forth.