LINEAR ALGEBRA WITH STRING DIAGRAMS
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...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/55157 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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