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This book is based on three undergraduate and postgraduate courses taught by the author on Matrix theory, Probability theory and Antenna theory over the past several years.
It discusses Matrix theory, Probability theory and Antenna theory with solved problems. It will be useful to undergraduate and postgraduate students of Electronics and Communications Engineering.
Matrix Theory
Perequisites of Linear Algebra
Quotient of a Vector Space
Triangularity of Comuting Operators
Simultaneous Diagonability of a Family of Comuting Normal Operators wrt an onb in a Finite Dimensional Complex Inner Product Space
Tensor Products of Vectors and Matrices
The Minimax Variational Principle for Calculating all the Eigenvalues of a Hermitian Matrix
The Basic Decompostition Theorems of Matrix Theory
A Computational Problems in Lie Group Theory
Primary Decompostition Theorem
Existence of Cartan Subalgebra
Exercises in Matrix Theory
Conjugancy Classes of Cartan Subalgebras
Exercises
Appendix: Some Applications of Matrix Theory to Control Theory Problems
Controllability of Supersymmetric Field the Oretic Problems
Controllability of Yang-Mills Gauge Fields in the Quantum Context Using Feynman’s Path Integral Approach to Quantum Field Theory
Large Deviations and Control Theory
Approximate Contollability of the Maxwell Equations
Controllability Problems in Quantum Scatering Theory
Kalman’s Notion of Controllability and Its Extension to pde’s
Controllability in the Context of Representations of Lie Groups
Irreducible Representations and Maximal Ideals
Controllability of the Maxwell-Dirac Equations Using External Classical Current and Field Sources
Controllability of the EEG Signals on the Brain Surface Modeled as a Spherical Surface by Influencing the Infinitesimal Dipoles in the Cells of the Brain Cortex to Vary in Accord to Sensory Perturbations
Control and Relativity
Probability Theory
The Basic Axioms of Kolmogorov
Exercises
Exercises on Stationary Stochastic Processes, Spectra and Polyspectra
A Research Problem Based on Problem
Exercises on the Construction of the Integral wrt a Probability Measure
Exercises on Stationarity, Dynamical Systems and Ergodic Thery
Antenna Theory
Course Outline
The Far Field Poynting Vector
Exercises
Order of Magnitudes in quantum Antenna Theory
The Notion of a Fermionic Coherent State and its Application to the Computation of the Quantum Statistical Moments of the Quantum Electromagnetic Field Generated by Electrons and Positors Within a Quantum Antenna
Calculating the Moments of the Radiation Field Produced by Electrons and Positrons in the Far Field when the Fermions are in a Coherent State
Controlling the Classical em Fields Interacting with the Dirac Field so that the Mean Value of the em Field Radiated by the Resulting Dirac Second Quantized Current in a Fermionic Coherent State is as Close as Possible to a Given Deterministic Pattern in Space and Simultaneously the Mean Square Fluctuations of this Field in a Fermionic Coherent State are Minimized
Approximate Analysis of a Rectangular Quantum Antenna
Remark on the Perturbation in the Quantum Dirac Field and the Quantum Electromangetic Field Interacting with Each Other Caused by Further Interaction of the Dirac Field with a Classical Control em Field and Interaction of the Quantum Electromagnetic Field with a Control Classical Current
Quantum Antennas Constructed Using Supersymmetric Field Theories
Quantization of the Maxwell and Dirac Field in a Background Curved Metric of Spacetime
Relationship Between the Electron Self Energy and the Electron Propagator
Electron Self Energy Corrections Induced by Quantum Gravitational Effects
Miscellaneous Problems
A Problem in Robotics
More on Root Space Decompostion of a Semisim-ple Lie Algebra
A Project Proposal for Developing an Ex-perimental Setup for Transmitting Quantum States Over a Channel in the Presence of An Eavesdropper
A Problem in Lie Group Theory
More Problems in Linear Algebra and Functional Analysis
Riesz Representation Theorem
Lie’s Theorem on Solvable Lie Algebras
Engel’s Theorem on nil-representation of a Lie Algebra
Aperture Antenna Pattern Fluctuations
Spectral Theorem Using Gelfand-Naimark Theorem
The Atiyah-Singer Index Theorem: A supersymmetric Proof
Replicas, Regular Elements, Jordan Decomposition and Cartan Subalgebras
Lecture Plan, Matrix Theory
More Assignment Problems in Probability Theory
Multiple Choice Questions on Probability Theory
Design of a Quantum Unitary Gate Using Superstring Theory with Noise Analysis Based on the Hudson-Parthasarathy Quantum Stochastic Calculus
Study Projects in Probability Theory: Construction of Brownian Motion, Law of the Iterarted Logarithm
Quantum Boltzmann Equation for a Systerm of Particles Interacting with a Quantum Electromagnectic Field
Device Physics in a Semiconductor Using the Classical Boltzmann Transport Equation
Describing the Value of a Point Charge and Its Location in Space in Terms of the Electrostatic Potential Generated by It
Calculating the Masses of N Gravitating Particles and Their Postitons and Their Trajectories from Measurement of the Gravitational Potential Distribution in Space-time Using the Newtonian Theory
The Quantum Boltzmann Equation for a Plasma
Some Other Remarks on Lie Algebras
Question Paper on Matrix Theory
Study Project on Quantum Antennas
Heat and Mass Transfer Equations in a Fluid
Quantum Electodynamics in a Background Medium Described by a Permittivity and Permeability Function
Temperature and Field Dependence of Re-fractive Index
Quantum Statistical Field Theory
Root Space Decompositions of the ComplexClassical Lie Algebras
Models for the Refractive Index of Materials and Liquids
Quantum Electrodynamics with the Electronic Charge Expressed in Terms of the Quantum Fields
Calculating the Masses of N Gravitating Paticles and Their Positions and Their Trajectories from Measurement of the Gravitational Potential Distribution in Space-time Using the Newtonian Theory
The Quantum Boltzmann Equation for a Plasma
Quantum Electrodynamics in a Background Medium Described by a Permittivity and Per-meability Function
Models for the Refractive Index of a Material Based on Classical and Quantum Physics
Quantum Statistical Field Theory
Relating the Refractive Index of a Material to the Metric Tensor of Space-time
Cosmologiccal Effects on the Refractive Index
More Problems in Probability Theory, Antennas and Refractive Index of Materials
Levy’s Modulus of Continuity for Brownian Motion
Test : Antennas and Wave Propagation
Article Submitted to the Quantum Information Processing Journals for Publication