Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.
Covers state vectors, Dirac notation, eigen-kets, and Hermitian operators in quantum physics.
Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.
Covers the exponential of operators and matrices, commutation properties, Jordan normal form, and linear algebra concepts related to linear operators and eigenvalue problems.
Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.
Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.
Explores discrete and continuous degrees of freedom, canonical commutation relations, and the correspondence between classical and quantum mechanics.
Explores eigenvalues, eigenvectors, and methods for solving linear systems with a focus on rounding errors and preconditioning matrices.
