• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.297-310
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• 2005

The concept of the Moore-Penrose inverse in an indefinite inner product space is introduced. Extensions of some of the formulae in the Euclidean space to an indefinite inner product space are studied. In particular range-hermitianness is completely characterized. Equivalence of a weighted generalized inverse and the Moore-Penrose inverse is proved. Finally, methods of computing the Moore-Penrose inverse are presented.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.691-706
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• 2020

Necessary and sufficient conditions are provided under which the weighted Moore-Penrose inverse A^†_MN exists, where A is an adjointable operator between Hilbert C^⁎-modules, and the weights M and N are only self-adjoint and invertible. Relationship between weighted Moore-Penrose inverses A^†_MN is clarified when A is fixed, whereas M and N are variable. Perturbation analysis for the weighted Moore-Penrose inverse is also provided.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.95-112
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• 2006

In this paper, the authors investigate the condition number with their condition numbers for weighted Moore-Penrose inverse and weighted least squares solution of min /Ax - b/M, where A is a rank-deficient complex matrix in $C^{m{\times}n} $ and b a vector of length m in $C^m$, x a vector of length n in $C^n$. For the normwise condition number, the sensitivity of the relative condition number itself is studied, the componentwise perturbation is also investigated.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.127-146
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• 2007

From 1876 to 1883, British mathematician James Joseph Sylvester worked as the founding head of Mathematics Department at the Johns Hopkins University which has been known as America's first school of mathematical research. Sylvester established the American Journal of Mathematics, the first sustained mathematics research journal in the United States. It is natural that we think this is the most exciting and important period in American mathematics. But we found out that the International Congress of Mathematicians held at the World's Columbian Exposition in Chicago, August 21-26, 1893 was the real turning point in American's dedication to mathematical research. The University of Chicago was founded in 1890 by the American Baptist Education Society and John D. Rockefeller. The founding head of mathematics department Eliakim Hastings Moore was the one who produced many excellent American mathematics Ph.D's in early stage. Many of Moore's students contributed to build up real American mathematics research power in early 20 century The University also has a well-deserved reputation as the "teacher of teachers". Beginning with Sylvester, we analyze what E.H. Moore had done as a teacher and a head of the new department that produced many mathematical talents such as L.E. Dickson(1896), H. Slaught(1898), O. Veblen(1903), R.L. Moore(1905), G.D. Birkhoff(1907), T.H. Hilderbrants(1910), E.W. Chittenden(1912) who made the history of American mathematics. In this article, we study how Moore's vision, new system and new way of teaching influenced American mathematical society at early stage of the top class mathematical research. and the meaning that early University of Chicago case gave.

• Korean Institute of Interior Design Journal
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• v.15 no.3 s.56
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• pp.92-101
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• 2006

This study examines placeness of the living space on the basis of Schulz's existential space and inquires into the expressional features of placeness by analyzing cases. Results of this study have shown that placeness of living space is formed by three factors as follows. First, the living space with placesness maintains inner order which structuralizes surroundings. Second, it expresses its identity through innate shape that reflects surroundings. Third, inner space has innate identity and it is much related to characteristics personality of a resident, environmental and psychological factors. It is as follows that concrete features of existential placeness shown in analyzing cases of Botta and Moore's works. There are concrete expressional features of placeness in the housing of Botta, and one is to keep order of inner space the horizontal and vertical axis reflected surroundings. Another is to show existence feeling as the shape of a stable singular mass with surroundings and regional properties. The third is to value innate features of each space inside housing and particularly to acquire placeness as combining phenomenological characteristic of light. There are concrete expressional features of placeness in the housing of Moore, and first, strong centrality formed in the inside is emphasized as extending to outside environment. Second, existence feeling is acquired as familiar form using the shape and material considered surroundings. Third, the personality of a resident is positively reflected in the design. Besides, placeness is acquired by goods and furniture as positively considering environmental and psychological sides.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.547-563
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• 2020

We define a left quotient as well as a right quotient of two bounded operators between Hilbert spaces, and we parametrize these two concepts using the Moore-Penrose inverse. In particular, we show that the adjoint of a left quotient is a right quotient and conversely. An explicit formulae for computing left (resp. right) quotient which correspond to adjoint, sum, and product of given left (resp. right) quotient of two bounded operators are also shown.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.251-258
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• 2015

Let $\mathcal{A}$ be a unital $C^*$-algebra, a, x and y are elements in $\mathcal{A}$. In this paper, we present the expression of the Moore-Penrose inverse and the group inverse of a-$xy^*$ under the conditions $x=aa^+x,y^*=y^*a^+a$, respectively.

• Journal of the Korean Mathematical Society
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• v.39 no.6
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• pp.963-973
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• 2002

We study torsion phenomena in the integral cohomology of finite if-spaces X through the Eilenberg-Moore spectral sequence converging to H＊($\Omega$X; Z$_{p}$). We also investigate how the difference between the Z$_{p}$-filtration length f$_{p}$(X) and the Z$_{p}$-cup length c$_{p}$(X) on a simply connected finite H-space X is reflected in the Eilenberg-Moore spectral sequence converging to H＊($\Omega$X;Z$_{p}$). Finally we get the following result: Let p be an odd prime and X an n-connected finite H-space with dim QH＊ (X;Z$_{p}$) $\leq$ m. Then H＊(X;Z) is p-torsion free if (equation omitted).tion omitted).

• Korean Journal of Logic
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• v.17 no.2
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• pp.287-322
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• 2014

We put forward a scheme of the theory of analysis, and G. E. Moore's theory of analysis is reconstructed. As C. H. Langford pointed out, Moore's theory commits to the paradox of analysis which says that if a analysis is correct then it is not informative, and if it is informative it is not correct. For, according to his theory, analysing statement is necessarily true identity statement and have some information. Moorean responses which is given by Max Black, Raymond Bradley and Norman Swartz, and Wilfrid Sellars rely on the distinction between the information about concepts and linguistic entity. These approaches are deficient in dealing properly with the difference in concepts as analysandum and analysans. Also, non-Moorean resolutions asserted by Myers, King, Black, and Earl are examined.

• Economic and Environmental Geology
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• v.46 no.1
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• pp.1-9
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• 2013

We proposed the revised full-pattern-fitting method of illite polytype quantification with background correction and scale factor correction of WILDFIRE(C) simulated pattern, and R% value ((${\sum}$|simulated-measured|/simulated)/ $n{\times}100$) calculation, and then verified the reliability of this method by applying for the test sample ($2M_1$:1M$$\frac{._-}{.}$$1:1), and by comparing the result with Grathoff and Moore method (1996). We confirmed that the proposed method showed the error range of less than 3.6%, which is much lower than the previous full-pattern-fitting methods, in spite of the impurities of the test sample. In the comparison with Grathoff and Moore method for 2 tested samples, we obtained the relatively higher $2M_1$ contents using Grathoff and Moore method, whereas we obtained the reliable results with less than 10% of R% values.