### Abstract

Our theories formalise various matrix properties that serve to establish existence, uniqueness and characterisation of the solution to affine systems of ordinary differential equations (ODEs). In particular, we formalise the operator and maximum norm of matrices. Then we use them to prove that square matrices form a Banach space, and in this setting, we show an instance of Picard-Lindelöf’s theorem for affine systems of ODEs. Finally, we use this formalisation to verify three simple hybrid programs.

### License

BSD License

### Topics

- Mathematics/Analysis
- Mathematics/Algebra

### Session Matrices_for_ODEs

- MTX_Preliminaries
- MTX_Norms
- SQ_MTX
- MTX_Flows
- MTX_Examples

### Depends on

- Verification Components for Hybrid Systems

### Auto-related entries

- The Poincaré-Bendixson Theorem
- Ordinary Differential Equations

## Cite

×

Matrices_for_ODEs-AFP

    @article{Matrices_for_ODEs-AFP,
      author  = {Jonathan Julian Huerta y Munive},
      title   = {Matrices for ODEs},
      journal = {Archive of Formal Proofs},
      month   = {April},
      year    = {2020},
      note    = {\url{https://isa-afp.org/entries/Matrices_for_ODEs.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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