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About 10,000 papers for “Matrix algebra”
David Machin · Biomathematics · 1976
This chapter describes sufficient basic matrix algebra to allow one to understand and manipulate problems expressed in matrix terms. The basic techniques described include addition, multiplication, inversion and the calculation of eigenvalues and their associated eigenvectors. Transition matrices are also discussed and their use illustrated by a simplified stable age distribution problem.
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Physical Oceanography · 2012
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James E. Gentle · Springer texts in statistics · 2007
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2006
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H. Yanai, Hideki Ishii · Elsevier eBooks · 2010
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Martin Anthony, Norman Biggs · Cambridge University Press eBooks · 2024
Accessible, concise, and interactive, this book introduces the mathematical methods that are indispensable in economics and finance. Fully updated to be as student friendly as possible, this edition contains extensive problems, worked examples and exercises (with full solutions at the end of the book). Two brand new chapters cover coupled systems of recurrence/differential equations, and matrix diagonalisation. All topics are motivated by problems from economics and finance, demonstrating to students how they can apply the mathematical techniques covered. For undergraduate students of economics, mathematics, or both, this book will be welcomed for its clarity and breadth and the many opportunities it provides for readers to practise and test their understanding.
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Elsevier eBooks · 2025
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Geoff Renshaw · Oxford University Press eBooks · 2021
This chapter shows how matrix algebra can help overcome the problems in solving a set of three or more simultaneous equations and how it makes it possible to handle large sets of simultaneous linear equations. It concludes by illustrating the applications of matrix algebra. First, to a simple macroeconomic model, showing how the methodology and notation can reveal in a very transparent way much about the relationships between variables and the effects of parameter changes. Second, to analyse inter-industry dependencies and the relationship between gross and net outputs in an economy.
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WORLD SCIENTIFIC eBooks · 1991
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Tomas B. Co · Cambridge University Press eBooks · 2013
In this chapter, we review some definitions and operations of matrices. Matrices play very important roles in the computation and analysis of several mathematical problems. They allow for compact notations of large sets of linear algebraic equations. Various matrix operations such as addition, multiplication, and inverses can be combined to find the required solutions in a more tractable manner. The existence of several software tools, such as MATLAB, have also made it very efficient to approach the solution by posing several problems in the form of matrix equations. Moreover, the matrices possess internal properties such as determinant, rank, trace, eigenvalues, and eigenvectors, which can help characterize the systems under consideration.
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Andreas Tilevik · 2025
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Delatorre, Anthony R., Cooke, William K. · Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School) · 1998
This thesis is designed to act as an instructor's supplement for refresher matrix algebra courses at the Naval Postgraduate School (NPS). The need for a beginning matrix algebra supplement is driven by the unique circumstances of most NPS students. Most military students attend XPS several years after receiving their undergraduate degrees. This supplement, unlike most college textbooks, bridges the gap between the student's educational lay-off and the rigors of mathematically oriented degrees such as applied math, operations research and engineering. By reviewing the fundamental concepts of vectors and matrices, and performing basic operations with them, the student quickly develops the background needed in NPS's demanding curriculums. This supplement focuses on matrix and vector operations, linear transformations, systems of linear equations, and computational techniques for solving systems of linear equations. The goal is to enhance current matrix algebra textbooks and help the beginning student build a foundation for higher level engineering and mathematics based courses.
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Alvin C. Rencher · Wiley series in probability and statistics · 2002
It would be difficult to write a book on multivariate analysis without the compact notation provided by matrix algebra. This chapter introduces all the matrix algebra needed to read the book. A few proofs are given where they seemed instructive, and most techniques are illustrated numerically. A large problem set provides additional numerical illustrations and practice in algebraic manipulations. The level of presentation does not assume that the reader has had previous exposure to matrix notation, although it would be helpful. Those without prior familiarity with matrices would need to work most of the problems in order to be comfortable with the notation used in the book.
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Bryan F. J. Manly, Jorge Alberto, Ken Gerow · 2024
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Elsevier eBooks · 2025
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2009
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K. A. Stroud · 1996
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Phoebus J. Dhrymes · 1978
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Alvin C. Rencher, G. Bruce Schaalje · 2007
This chapter contains sections titled: Matrix and Vector Notation Operations Partitioned Matrices Rank Inverse Positive Definite Matrices Systems of Equations Generalized Inverse Determinants Orthogonal Vectors and Matrices Trace Eigenvalues and Eigenvectors Idempotent Matrices Vector and Matrix Calculus Problems
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S. M. Blinder · Elsevier eBooks · 2013
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