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International Journal for Research Trends and Innovation
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ISSN Approved Journal No: 2456-3315 | Impact factor: 8.14 | ESTD Year: 2016
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| Paper Title: | Best Generalized inverse of Linear operator in Normed affine space |
| Authors Name: | V. Vijayaselvi , D. Krishnaswamy |
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IJRTI_180480
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| Published Paper Id: | IJRTI1809031 |
| Published In: | Volume 3 Issue 9, September-2018 |
| DOI: | |
| Abstract: | Let $X$,$Y$ be normed affine space $A(X,Y)$ be a bounded linear operator from $X$ to $Y$ one wants to solve the linear problem $Ax=y$ for $x$ (given $y in Y$). When $A$ is invertible the unique solution is $x=A^{-1}y$. If this is not the case, one seeks an approximate solution of the form $x=By$, where $B$ is an operator from $Y$ to $X$ such $B$ is called generalized inverse of $A$. Given an affine space $E$ of dim n and an affine frame $(a_{0},a_{1}cdots a_{m})$ for $E$. Let $f:E ightarrow E$ and $g:E ightarrow E$ be two affine maps represented by the two $(n+1) imes (n+1)$ matrices $egin{bmatrix} A & b 0 &1 end{bmatrix}$ and $egin{bmatrix} B & c 0 & 1 end{bmatrix}$ with respect to the frame $(a_{0},a_{1}cdots a_{m})$ we also say that $f$ and $g$ represented by $(A,b)$ and $(B,c)$. In this paper we prove that $f$ is invertible if and only if $A$ is invertible and the solution exists in a unique way. |
| Keywords: | Affine space, Linear operator, Affine linear Transformation |
| Cite Article: | "Best Generalized inverse of Linear operator in Normed affine space ", International Journal for Research Trends and Innovation (www.ijrti.org), ISSN:2455-2631, Vol.3, Issue 9, page no.193 - 196, September-2018, Available :http://www.ijrti.org/papers/IJRTI1809031.pdf |
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2456-3315 | IMPACT FACTOR: 8.14 Calculated By Google Scholar| ESTD YEAR: 2016 An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 8.14 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator |
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Published Paper ID: IJRTI1809031
Registration ID:180480
Published In: Volume 3 Issue 9, September-2018
DOI (Digital Object Identifier):
Page No: 193 - 196 Country: cuddalore, Tamil Nadu, India Research Area: Applied Mathematics Publisher : IJ Publication Published Paper URL : https://www.ijrti.org/viewpaperforall?paper=IJRTI1809031 Published Paper PDF: https://www.ijrti.org/papers/IJRTI1809031 |
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ISSN: 2456-3315
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