Vector Algebra, straight lines and planes, surfaces and curves in space, basic 2nd order surfaces. Matrices, Determinants, Linear systems, Eigenvalues, eigenvectors of matrices, Diagonalization of matrices , Cayley-Hamilton theorem. Vector spaces, subspaces, basis and dimension of vector spaces. Linear maps, Inner product vector spaces, Orthonormal bases, Orthogonal complement. Self-adjoint and isometric transformations and their matrices.