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Categories for Quantum TheoryAn Introduction$
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Chris Heunen and Jamie Vicary

Print publication date: 2019

Print ISBN-13: 9780198739623

Published to Oxford Scholarship Online: January 2020

DOI: 10.1093/oso/9780198739623.001.0001

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Linear Structure

Linear Structure

Chapter:
(p.61) 2 Linear Structure
Source:
Categories for Quantum Theory
Author(s):

Chris Heunen

Jamie Vicary

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198739623.003.0002

Many aspects of linear algebra can be reformulated as categorical structures. This chapter examines abstractions of the base field, zero-dimensional spaces, addition of linear operators, direct sums, matrices, inner products and adjoints. These features are essential for modelling features of quantum theory such as superposition, classical data and measurement.

Keywords:   Scalar, Superposition, Biproduct, Dagger, Kernel, Matrix

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