Formalization of Infinite Dimension Linear Spaces with Application to Quantum Theory

  • Mohamed Yousri Mahmoud
  • Vincent Aravantinos
  • Sofiène Tahar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7871)


Linear algebra is considered an essential mathematical theory that has many engineering applications. While many theorem provers support linear spaces, they only consider finite dimensional spaces. In addition, available libraries only deal with real vectors, whereas complex vectors are extremely useful in many fields of engineering. In this paper, we propose a new linear space formalization which covers both finite and infinite dimensional complex vector spaces, implemented in HOL-Light. We give the definition of a linear space and prove many properties about its operations, e.g., addition and scalar multiplication. We also formalize a number of related fundamental concepts such as linearity, hermitian operation, self-adjoint, and inner product space. Using the developed linear algebra library, we were able to implement basic definitions about quantum mechanics and use them to verify a quantum beam splitter, an optical device that has many applications in quantum computing.


Linear Space Linear Algebra Beam Splitter Scalar Multiplication Computer Algebra System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mohamed Yousri Mahmoud
    • 1
  • Vincent Aravantinos
    • 1
  • Sofiène Tahar
    • 1
  1. 1.Electrical and Computer Engineering Dept.Concordia UniversityMontrealCanada

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