LINEAR ALGEBRA WITH STRING DIAGRAMS

• Main Author: Gunawan, Rubio
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/55157
• Institution: Institut Teknologi Bandung

A category is an algebraic structure consisting of a collection of objects and a collection of morphisms from objects to objects. Morphisms can be composed, and the composition is associative. A common type of category are PROPs (Product and Permutation Category). PROPs have additional structures, which are a product operation between two morphisms, and the existence of morphisms that correspond to permutations. The PROPS that are relevant to this final project are MatZ which has integer matrices as morphisms, and SVQ which has linear relations from Qn to Qm as morphisms. String diagrams or circuits are diagrams that are used to represent morphisms of PROPs visually. Formally, it is possible to construct a PROP isomorphic to the PROP that we want to represent, using circuits as morphisms. This final project will explore how circuits that represent PROPs can be used to give a visual representation of several concepts in linear algebra, by representing MatZ and SVQ. In particular, an extension of the rational number system will be obtained, and a visual representation of the orthogonal projection to the image of a matrix as a diagram will be obtained.