Lectures related to Matrix exponential

Asymptotic States and S-matrix

Covers the concept of asymptotic states and S-matrix in quantum field theory, focusing on the evolution of wave packets and the scattering states.

Asymptotic States and S-matrix: Operators

Explores asymptotic states, S-matrix, and operators in quantum field theory, emphasizing the role of discrete symmetries and complete sets of states.

Asymptotic States and S-matrix

Explores asymptotic states, S-matrix, Lippmann-Schwinger equation, and energy robustness in quantum field theory.

Discrete Symmetries: Asymptotic States and S-matrix

Covers the concept of discrete symmetries, focusing on the introduction to asymptotic states and S-matrix.

Linear Algebra: Matrix Operations

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Elementary Matrices and Inverses

Covers elementary matrices, their properties, and the algorithm to find the inverse of a matrix.

Systems of n linear ODEs with constant coupling matrix A

Covers systems of n linear first-order ODEs with constant coupling matrix A and explores properties of solutions and the superposition principle.

Symmetric and Anti-symmetric Matrices

Introduces symmetric and anti-symmetric matrices, matrix powers, inverses, elementary matrices, and matrix manipulation.

Matrix Equations and Homogeneous Systems

Explores matrix equations, homogeneous systems, solutions, consistency, and properties.

SISO Polynomial Controllers: Sylvester Matrix, Internal Model Principle

Covers the design of SISO polynomial controllers using concepts such as the Sylvester matrix and model matching.

Matrix Equation Resolution

Covers the resolution of a system of equations using the Gramer rule.

Signals & Systems I: Preliminary Concepts and Linear Systems

Covers preliminary concepts in signals and systems, including linear systems invariant in time and stability.

Diagonalization: Criteria and Examples

Covers the criteria for diagonalizing a matrix and provides illustrative examples.

Power Systems Dynamics

Covers transient stability, power flow analysis, and load flow methods in power systems.

Matrix Exponential: Properties and Convergence

Explores the properties and convergence of the matrix exponential for linear systems.

Matrix Functions: Theory and Computation

Covers the theory and computation of matrix functions, focusing on computing f(A) and particularly e^A, with special attention to the matrix exponential and common examples of matrix functions.

Principles of Quantum Mechanics

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

QED: Gauge Theories

Covers Quantum Electrodynamics (QED), instantons, Feynman rules, and gauge theories in modern particle physics.

Matrix Equations: Finding Free Variables

Explains how to find free variables in matrix equations and analyze characteristic polynomials.

Matrix Operations: Definitions and Examples

Covers the basic operations on matrices, including addition, scalar multiplication, and matrix multiplication.