Abstract :

Tensor Products Are Fundamental Constructions In Linear Algebra, Abstract Algebra, And Modern Mathematical Physics. They Provide A Universal Framework For Studying Bilinear Mappings And Have Extensive Applications In Multilinear Algebra, Representation Theory, Differential Geometry, And Quantum Information Theory. This Paper Presents An Overview Of The Construction Of Tensor Products Of Vector Spaces, Discusses Their Fundamental Properties, And Illustrates Selected Applications Through Examples. The Exposition Is Intended As A Concise Reference For Graduate Students And Researchers Entering The Field. Topological Vector Spaces (TVSs) Provide A Framework That Unifies Algebraic And Topological Structures, Playing A Central Role In Functional Analysis. Tensor Products Of Topological Vector Spaces Extend Multilinear Mappings Into Linear Mappings And Have Applications In Distribution Theory, Operator Theory, And Quantum Mechanics. This Paper Reviews The Fundamental Concepts Of Topological Vector Spaces And Tensor Products, Discusses Projective And Injective Tensor Product Topologies, And Presents Several Illustrative Examples And Basic Properties. Keywords: Tensor Product, Vector Space, Bilinear Map, Multilinear Algebra, Universal Property. Topological Vector Spaces, Tensor Products, Locally Convex Spaces, Projective Topology, Injective Topology, Functional Analysis.

Published:

07-8-2026

Issue:

Vol. 26 No. 8 (2026)

Page Nos:

811 - 817

Section:

Articles

License:

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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