Lecture 12 of 47Week 3
Linear Algebra - Change of Basis and Similarity Transformation
Prof. Ramkrishna Pasumarthy · IIT Madras
Credits and licence
- From
- Linear Systems Theory, IIT Madras (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
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All the lectures
- Introduction to Linear Systems
- System Models - Part 01
- System Models - Part 02
- System Models - Part 03
- General Representation
- Sets, Functions and Fields
- Linear Algebra - Vector Spaces and Metric Spaces
- Linear Algebra - Span, Basis and Subspaces
- Linear Algebra - Linear Maps and Matrices
- Linear Algebra - Fundamental Subspaces and Rank-Nullity
- Tutorial 1 on Linear Algebra
- Linear Algebra - Change of Basis and Similarity Transformation
- Linear Algebra - Invariant Subspaces, Eigen Values & Eigen Vectors
- Linear Algebra - Diagonalization and Jordan Forms
- Linear Algebra - Eigen Decomposition and Singular Value Decomposition
- Tutorial 2 on Linear Algebra
- Solutions to LTI Systems
- State Transition Matrix for LTI systems
- Forced Reponse of Continuous and Discrete LTI system
- State Transition Matrix and Solutions to LTV systems
- Equilibrium Points
- Limit Cycles and Linearisation
- Stability Analysis & Types of Stability
- Lyapunov Stability
- Stability of Discrete Time Systems
- Supplementary Lecture: Comparison Lemma and Lyapunov Stabilty
- Controllability and Reachability
- Controllability Matrix and Controllable Systems
- Controllability Tests
- Controllability of Discrete Time Systems
- Controllable Decomposition
- Stabilizability
- Observability
- Gramians and Duality
- Observability for Discrete Time Systems and Observability Tests
- Observable Decompositon and Detectability
- Kalman Decomposition and Minimal Realisation
- Canonical Forms and State Feedback Control
- Control Design using Pole Placement
- Tutorial for Modules 9 and 10
- State Estimation and Output Feedback
- Design of Observer and Observer based Controller
- Optimal Control and Linear Quadratic Regulator (LQR)
- Feedback Invariant and Algebraic Ricatti Equation
- Tutorial for Module 11
- Linear Matrix Inequalities
- Properties of LMIs and Delay LMIs