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Paper Title: Best Generalized inverse of Linear operator in Normed affine space
Authors Name: V. Vijayaselvi , D. Krishnaswamy
Unique Id: IJRTI1809031
Published In: Volume 3 Issue 9, September-2018
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 of Science & Engineering Development Research (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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Publication Details: Published Paper ID: IJRTI1809031
Registration ID:180480
Published In: Volume 3 Issue 9, September-2018
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ISSN Number: 2456 - 3315
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