The Representation of Matrices in Unit Vector Notation


  •  Abhimanyu Pallavi Sudhir    

Abstract

The objective of this paper is to express a matrix of any dimension in unit vector notation. This is accomplished by first solving the two and three dimensional cases before solving the general n-dimensional case. The fact that matrices can be represented as a (non-linear) combination of standard basis unit vectors shows that matrices are not simply abstract entities used just for representing data, but also have a geometric interpretation. This paper then defines the natural product and explains its applications in matrix calculus, before relating it to the outer product of real vectors, a special case of the tensor product. We then conclude that the space is the intersection of the exterior space and the newly defined \textit{natural space}.



This work is licensed under a Creative Commons Attribution 4.0 License.
  • ISSN(Print): 1916-9795
  • ISSN(Online): 1916-9809
  • Started: 2009
  • Frequency: bimonthly

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