Lecture
Linear Algebra: Vector Spaces & Operators
Related lectures (36)
Vector Spaces: Properties and Operations
Covers the properties and operations of vector spaces, including addition and scalar multiplication.
Linear Algebra in Dirac Notation
Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.
Matrix Diagonalization: Spectral Theorem
Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.
Decomposition Spectral: Symmetric Matrices
Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.
Postulates of Quantum Mechanics
Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.
Diagonalization of Linear Transformations
Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.
Diagonalization of Linear Transformations
Covers the diagonalization of linear transformations in R^3, exploring properties and examples.
Spectral Decomposition of Bounded Self-Adjoint Operators
Explores the spectral decomposition of self-adjoint operators on Hilbert spaces.
Eigenvalue problem: Eigenbasis, Spectral theorem
Explores eigenvalue problems, eigenbasis, spectral theorem, and properties of normal operators.
Adjoint of Linear Operators on Inner Product Spaces
Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.