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Enkhmurun Bayasgalan

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Matrix Theory
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Notation and Nomenclature

Enkhmurun Bayasgalan

Home
Matrix Theory
Matrix Theory
- References
- Norms
  Norms
  - Vector Norms
  - Matrix Norms
- Matrix Factorization
  Matrix Factorization
- Matrix Calculus
  Matrix Calculus
  - Identities
  - Matrix Calculus
- Software Implementation
  Software Implementation
  - Storage
  - Multiplication
Kinematics
Kinematics
- Rotations and Cross-Relations
  Rotations and Cross-Relations
- Lie Group and Lie Algebra
  Lie Group and Lie Algebra
- Jacobians
  Jacobians
- Optimization on Smooth Manifolds
  Optimization on Smooth Manifolds
  - Interpolation
  - Difference of Rotations
- Cartesian Position
- Velocity
- Acceleration
- Camera Motion
  Camera Motion
  - Camera Pose
- References
Estimation Theory
Estimation Theory
- References
- Probability Theory
  Probability Theory
- Optimization
  Optimization
  - Sets
    Sets
    
    Norms, Distance, and Unit Ball
    
    Open and Closed Sets
    
    Geometry
    
    Convex Sets
    
    Nonconvex Sets
  - Functions
    Functions
    
    Functions, Gradient, Jacobian, Hessian
    
    Convex Functions
    
    Nonconvex Functions
  - Optimization Problem Formulation
  - Duality Theory
  - Unconstrained Optimization
    Unconstrained Optimization
    
    Optimality Conditions
    
    Gradient Desent
    
    Newton's Method
    
    Quasi-Newton Method
    
    Gauss-Netwon Method
    
    Golden Section
    
    Quadratic Fit
    
    Nelder-Mead Method
  - Linear Programming
    Linear Programming
    
    Modelling Using Linear Programs
    
    Algrebraic Aspects
    
    Simplex Method
    
    Linear Stochastic Program
    
    Nonlinear Program
    
    Robust Optimization
    
    Column and Constraint Generation
    
    Dantzig-Wolfe Decomposition
  - Nonlinear Programming
    Nonlinear Programming
    
    Least Squares
  - Perturbation Methods
  - Integer Programming
    Integer Programming
    
    Discrete Optimization Models
    
    Modelling Nonconvex Functions
    
    Modelling Nonconvex Sets
    
    Modelling Logical Relations
- Statistical Estimators
  Statistical Estimators
  - Moment-Matching Estimator
  - Maximum Likelihood Estimator
- Bayesian Inference
  Bayesian Inference
- Least Squares Estimator
  Least Squares Estimator
- Kalman Filter
  Kalman Filter
  - Discrete-Time Kalman Filter
- Extended Kalman Filter
  Extended Kalman Filter
  - Continuous-Time EKF
- Factor Graphs
  Factor Graphs
  - Definition
  - Representations
  - Using Factor Graph
    Using Factor Graph
    
    Simple Averaging
    
    Weighted Averaging
    
    Weighted Non-Linear Least Squares
    
    Dynamical Systems
Navigation
Navigation
- References
- Coordinate Frames
- Geodesy
  Geodesy
- IMU and Gravity Models
  IMU and Gravity Models
- Inertial Navigation
  Inertial Navigation
- Radio Positioning
  Radio Positioning
  - Position by Ranging
    Position by Ranging
    
    Ranging
    
    Positioning from Passive Ranging
  - Angular Position
  - Time Standards
- GPS
  GPS
Computer Vision
Computer Vision
- Termanologies
- Image Processing
  Image Processing
  - Correlation Filter
- Image Features
  Image Features
  - ORB
- Two-View Geometry
  Two-View Geometry
- Image Compression
  Image Compression
  - Compression via Low-Rank Matrix Approximation
Software
Software
- Concurrency
  Concurrency
  - OpenMP
    OpenMP
    
    Basic Usage
    
    Examples
    Examples
    
    Calculating PI
Sensors
Sensors
- GNSS
  GNSS
Papers
Papers
- Software
Notation and Nomenclature

References

Misra, P., Global Positioning System, 2nd Edition
Mahalati, R.N., EE259: Principles of Sensing for Autonomy, 2023