Results 21 to 30 of about 2,174,992 (257)
Proof of Cramer’s rule with Dirac delta function [PDF]
European Journal of Physics, 2020 Abstract We present a new proof of Cramer’s rule by interpreting a system of linear equations as a transformation of n-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the original coordinate vector with Dirac delta functions and changing integration variables from the ...
June-Haak Ee, Jungil Lee, Chaehyun Yu
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An effective and economic estimation of population mean in stratified random sampling using a linear cost function [PDF]
HeliyonImprovement in the estimation of population mean has been an area of interest in sampling theory. So many estimators have been suggested for elevated estimation of the population mean in stratified random sampling, but there is still a gap for more ...
Abdullah A. Zaagan +6 more
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Cramer’s rule for some quaternion matrix equations [PDF]
Applied Mathematics and Computation, 2010 13 ...
Ivan Kyrchei
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Journal of Fundamental and Applied Sciences, 2018 No AbstractKeywords: Cramer’s rule; determinant; system of linear ...
Babarinsa, O, Kamarulhaili, H
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Differential Thermal Inactivation Enables Simultaneous Quantitation of Ricin and Abrin [PDF]
ToxinsRicin and abrin are highly lethal Type II ribosome-inactivating proteins. They depurinate the same site of the 28S rRNA to inhibit protein synthesis. Consequently, standard molecular-level activity assays used to detect the toxic activity of ricin or ...
Woo-Hyeon Jeong
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A Generalization of Cramer’s Rule
Advances in Linear Algebra & Matrix Theory, 2015 In this paper, we find two formulas for the solutions of the following linear equation , where is a real matrix. This system has been well studied since the 1970s. It is known and simple proven that there is a solution for all if, and only if, the rows of A are linearly independent, and the minimum norm solution is given by the Moore-Penrose inverse ...
H. Leiva
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Old and new proofs of Cramer's rule
Applied Mathematical Sciences, 2014 In spite of its high computational cost, Cramer’s Rule for solving systems of linear equations is of historical and theoretical importance. In this paper we list six dierent proofs of it, the last of which has not apparently been published elsewhere. A discussion on their educational value and the tools involved is also included.
Maurizio Brunetti, R. Caccioppoli
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A graph theoretic proof of Cramer's rule
This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.
Sudip Bera
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Cramer's Rule in Hyperbolic Number Plane
Highlights in Science, Engineering and TechnologyThis paper investigates the existence theorem for solutions to hyperbolic linear systems and presents the judgment conditions for the existence of such solutions. It extends the judgment conditions applicable to general linear systems, expanding the research scope from real matrices, a focus in advanced algebra, to hyperbolic matrices.
Kangze Chen, Yuxin Wang, Yubo Wang
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Types of System of the neutrosophic linear equations and Cramer’s rule [PDF]
Neutrosophic Sets and Systems, 2021 The purpose of this article is studying the types of system of neutrosophic linear equations, where the neutrosophic linear equation and the solution to the neutrosophic linear equation are defined.
Yaser Ahmad Alhasan
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