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Quadratic form for a positive definite matrix.

Quadratic form for a positive definite matrix.

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Matrix theory plays a very important role in teaching Mathematics and solving mathematical problems. Studying the theory of matrix can help academics, practitioners, and students solve many problems in Engineering, Econometrics, Finance, Economics, Optimization, Decision Sciences, and many other areas. To review the matrix theory with applications,...

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... The matrix in which all the elements are zero is said to be a zero matrix [5]. ...
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When we take only the real constants of a linear equation or a system of linear equations and make an array then it becomes a matrix. There are different types of matrix which is identified and defined based on the structure consisting elements in different ways and existing in different positions. This research paper will briefly discuss on a matrix different from other types of matrix described in various books and papers. Some important properties and characteristics of this matrix are included in this paper.
... The following are well-known results [32,33]: ...
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The concept of smart cities emerged in the 1990s. Since then, smart buildings have become a closely interconnected element of smart cities. This type of building implements Internet of Things technology and control algorithms to monitor and control their indoor environment. The aim of this paper is to develop a new stability criterion method for smart building Internet of Things (IoT) systems, subject to external disturbances. The new stability criterion is going to optimize the operation of control algorithms since this criterion does not depend on the transmission function of the control algorithm but on the data collected by the IoT system. We present a new matrix called “Laplacian IoT matrix”, containing IoT network information associated with the graph of a smart building. The proposal is supported by the results of a numerical case study.
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Purpose: Text mining is a very important issue in Statistics, Applied Mathematics, and many other areas in Sciences, Engineering, and Business because its applications are extremely rich and varied. Text mining can help academics and practitioners with some specific issues such as spam filtering, personal background matching, sentiment analysis, document classification, etc. Design/methodology/approach: The statistical software R is an exceedingly widely used software in Science because of its outstanding and completely free features. To contribute to the literature related to text mining, this study provides detailed instructions on how to use the statistical software R for text mining. Findings: To implement this goal, we first introduce the algorithm for text mining. We then discuss how to use the software R to approach each step of the algorithm in detail. As an application, the proposed algorithm is studied with an actual data set. Originality/value: This study provides detailed instructions on how to use the statistical software R for text mining which is new in the literature. Implications: The results found in this study will help academics and practitioners understand how to use the statistical software R to analyze text mining. This paper is very useful for both academics and practitioners in the study of text mining.