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Everything about Matrix difference equation
Relation of a matrix of variables between two points in time
In mathematics, a matrix difference equation is a difference equation in which the value of a vector of variables at one point in time is related to its own value at one or more previous points in time using matrices. The order of the equation is the maximum time gap between any two indicated values of the variable vector. For example, Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Matrix difference equationA 5-minute orientation
- Skim a recent paper: A Note on Riccati Matrix Difference EquationsInfluential work since 2022
- Pick up a classic book: Modelli Dinamici DiscretiThe most-reprinted book on the subject
- Read the landmark paper: A Liapunov functional for a matrix difference-differential equationCited 134 times
- Go sideways: Rational difference equationA closely related topic
- Go sideways: Algebraic Riccati equationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
- Nonhomogeneous first-order case and the steady state
- Stability of the first-order case
- Solution of the first-order case
- Extracting the dynamics of a single scalar variable from a first-order matrix system
- Solution and stability of higher-order cases
- Nonlinear matrix difference equations: Riccati equations
🏆 Landmark papers (most cited)
A Liapunov functional for a matrix difference-differential equation
A Liapunov functional for a matrix neutral difference-differential equation with one delay
Matrix Difference Equation Analysis of Vibrating Periodic Structures
The basic Gauss hypergeometric matrix function and its matrixq-difference equation
The Stability Cone for a Matrix Delay Difference Equation
Numerical Solution of the Poisson Equation Using Finite Difference Matrix Operators
The Samuelson macroeconomic model as a singular linear matrix difference equation
Elliptic Kac–Sylvester Matrix from Difference Lamé Equation
🆕 Influential since 2022
A Note on Riccati Matrix Difference Equations
Solution of a discrete matrix equation with second-order difference and single delay
SOLVING SCHRÖDINGER EQUATION NUMERICALLY USING THE MATRIX FINITE DIFFERENCE METHOD
A Difference Equation Matrix Model Predictive Control Approach Applied to a Distillation Column
A Fuzzy Difference Equation Matrix Model for the Control of Multivariable Nonlinear Systems
📚 Books worth reading
Modelli Dinamici DiscretiErnesto Salinelli · 2009
Difference equationsPaul Cull, Mary Flahive · 2005- 📕Stability of Neutral Functional Differential EquationsMichael I. Gil' · 2014
- 📕Galois theories of linear difference equationsCharlotte Hardouin · 2016
- 📕Discrete dynamical modelsErnesto Salinelli · 2014
Linear Algebra in Action
Graduate Studies in MathematicsHarry Dym · 2014- 📕Dynamical systems and linear algebraFritz Colonius · 2014
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Lyapunov equation The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical…
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