This module delves deeper into the topic of linearization, discussing techniques and applications in navigation through range measurement. It includes:
This module introduces the concept of linear dynamical systems, discussing their importance in various fields. It provides illustrative examples to showcase the application of linear functions in practical scenarios.
Key topics include:
This module continues the exploration of linear functions by providing various interpretations and applications. It covers examples from different domains including:
Additionally, it introduces concepts of linearization and first-order approximation of functions.
This module delves deeper into the topic of linearization, discussing techniques and applications in navigation through range measurement. It includes:
This module continues the discussion on the nullspace of matrices, covering essential concepts such as:
This module focuses on orthonormal sets of vectors, demonstrating their geometric interpretation and applications. Key topics include:
This module introduces the least-squares method, providing a geometric interpretation and explaining its significance in various contexts. Topics covered include:
This module addresses least-squares polynomial fitting, focusing on various methods and considerations in model identification. Key topics include:
This module expands on multi-objective least-squares, discussing how to minimize multiple objectives effectively. Topics include:
This module covers least-norm solutions, detailing methods to find solutions in underdetermined systems. It includes:
This module presents examples of autonomous linear dynamical systems, illustrating their practical applications. Key content includes:
This module explores solutions via the Laplace transform and matrix exponential methods. It covers:
This module focuses on the time transfer property, discussing system behavior over time. Topics include:
This module explores the application of Markov chains as an example of linear dynamical systems. It examines:
This module introduces the Jordan canonical form, explaining its significance in analyzing linear systems. Key topics include:
This module focuses on the DC or static gain matrix, discussing its role in system dynamics. It includes:
This module examines the RC circuit as an example, exploring quadratic forms and their implications. Key points include:
This module explores the concept of gain in a direction, providing insights into singular value decomposition (SVD) and its applications. Key topics include:
This module addresses the sensitivity of linear equations to data error, exploring concepts of low-rank approximations and model simplification. Topics include:
This module investigates reachability in linear dynamical systems, discussing controllable systems and minimum energy input requirements. Key themes include:
This final module addresses continuous-time reachability, emphasizing general state transfer and observability in linear systems. Topics include: