Quaternionic Hilbert spaces and operator theory

Quaternionic Hilbert spaces and operator theory

This report serves to study Hilbert spaces and operator theory over skew fields. In particular, we will study these topics over the quaternions since it has been well-developed, and explore the properties of quaternionic linear operators, adjoint and normal operators. Operators over quaternionic Hil...

Full description

Saved in:
Bibliographic Details
Main Author: Lim, Zhi Xing
Other Authors: Wu Guohua
Format: Final Year Project
Language:English
Published: Nanyang Technological University 2024
Subjects:
Mathematical Sciences
Hilbert spaces
Operator theory
Quaternions
Online Access:https://hdl.handle.net/10356/181339
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-181339
record_format dspace
spelling sg-ntu-dr.10356-1813392024-11-26T04:41:26Z Quaternionic Hilbert spaces and operator theory Lim, Zhi Xing Wu Guohua School of Physical and Mathematical Sciences guohua@ntu.edu.sg Mathematical Sciences Hilbert spaces Operator theory Quaternions This report serves to study Hilbert spaces and operator theory over skew fields. In particular, we will study these topics over the quaternions since it has been well-developed, and explore the properties of quaternionic linear operators, adjoint and normal operators. Operators over quaternionic Hilbert spaces are important when exploring certain topics, which include functional analysis, Fourier transform, and quantum mechanics. An application of operators over the quaternions is to rotate vectors in 3-dimensional space by conjugating said vectors with the axis of rotation. Bachelor's degree 2024-11-26T04:41:26Z 2024-11-26T04:41:26Z 2024 Final Year Project (FYP) Lim, Z. X. (2024). Quaternionic Hilbert spaces and operator theory. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/181339 https://hdl.handle.net/10356/181339 en application/pdf Nanyang Technological University
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Mathematical Sciences
Hilbert spaces
Operator theory
Quaternions
spellingShingle Mathematical Sciences
Hilbert spaces
Operator theory
Quaternions
Lim, Zhi Xing
Quaternionic Hilbert spaces and operator theory
description This report serves to study Hilbert spaces and operator theory over skew fields. In particular, we will study these topics over the quaternions since it has been well-developed, and explore the properties of quaternionic linear operators, adjoint and normal operators. Operators over quaternionic Hilbert spaces are important when exploring certain topics, which include functional analysis, Fourier transform, and quantum mechanics. An application of operators over the quaternions is to rotate vectors in 3-dimensional space by conjugating said vectors with the axis of rotation.
author2 Wu Guohua
author_facet Wu Guohua
Lim, Zhi Xing
format Final Year Project
author Lim, Zhi Xing
author_sort Lim, Zhi Xing
title Quaternionic Hilbert spaces and operator theory
title_short Quaternionic Hilbert spaces and operator theory
title_full Quaternionic Hilbert spaces and operator theory
title_fullStr Quaternionic Hilbert spaces and operator theory
title_full_unstemmed Quaternionic Hilbert spaces and operator theory
title_sort quaternionic hilbert spaces and operator theory
publisher Nanyang Technological University
publishDate 2024
url https://hdl.handle.net/10356/181339
_version_ 1816859035822981120

Similar Items