Lectures related to Uncertainty Principle

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Quantum Mechanics: Operators and Eigenvalues

Covers matrix elements, operators, paths with conditions, and time evolution in quantum mechanics.

Covers the principles of quantum mechanics, including the Measurement Principle and Max Born Rule.

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Linear Algebra: Reduction of Linear Application

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

Matrix Operations: Transposition, Rank, and Basis Change

Covers matrix transposition, rank, and basis change in linear algebra, exploring invertibility criteria and basis relationships.

Diagonalization of Linear Transformations

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Eigenvalues and Similar Matrices

Introduces eigenvalues, eigenvectors, and similar matrices, emphasizing diagonalization and geometric interpretations.

Linear Algebra: Quantum Mechanics

Covers the application of linear algebra concepts to Quantum Mechanics, including spectral theorem and Brillouin zone.

Diagonalization of Linear Transformations

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Linear Applications: Matrices and Transformations

Covers linear applications, matrices, transformations, and the principle of superposition.

Matrix Similarity and Diagonalization

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Matrix Eigenvalues and Eigenvectors

Covers matrix eigenvalues, eigenvectors, and their linear independence.

Linear Algebra: Basis and Matrices

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

Linear Transformations: Injective and Surjective

Explores injective and surjective linear transformations, kernel, image, and matrix operations.

Eigenvalues and Eigenvectors

Covers eigenvalues and eigenvectors, explaining their importance in linear algebra.

Linear Mapping and Bases

Explores linear mapping, isomorphism, and change of bases in vector spaces.

Quantum Physics I

Explores eigenvalues, ladder operations, and quantum number values in quantum physics.