Signal RepresentationsCovers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.
Normed SpacesCovers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Vector spaces: Hilbert spaceIntroduces vector spaces, bases, and the Hilbert space, highlighting the practical implications of defining a basis in a vector space.
Linear Algebra: Quantum MechanicsExplores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.
Vector Spaces EquivalenceExplores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.
Quantum States and OperatorsCovers the description of states in quantum mechanics and their relation to probability, expectation values, and the Schrödinger equation.
Vector Calculus in 3DCovers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.