degree of Bachelor of Commerce (Honours) in Economics‚ The University of Auckland‚ 2011. Abstract This dissertation‚ by making use of important geometric and econometric concepts such as a ‘linear manifold’‚ a ‘plane of support’‚ a ‘projection matrix’‚ ‘linearly estimable parametric functions’‚ ‘minimum variance estimators’ and ‘linear transformations’‚ seeks to explore the role of a Concentration Ellipsoid as a geometric tool in the interpretation of certain key econometric results connected
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Linear Least Squares Suppose we are given a set of data points {(xi ‚ fi )}‚ i = 1‚ . . . ‚ n. These could be measurements from an experiment or obtained simply by evaluating a function at some points. You have seen that we can interpolate these points‚ i.e.‚ either find a polynomial of degree ≤ (n − 1) which passes through all n points or we can use a continuous piecewise interpolant of the data which is usually a better approach. How‚ it might be the case that we know that these data points should
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and classes Key OpenCV Classes Point_ Point3_ Size_ Vec Matx Scalar Rect Range Mat SparseMat Ptr Template 2D point class Template 3D point class Template size (width‚ height) class Template short vector class Template small matrix class 4-element vector Rectangle Integer value range 2D or multi-dimensional dense array (can be used to store matrices‚ images‚ histograms‚ feature descriptors‚ voxel volumes etc.) Multi-dimensional sparse array Template smart pointer class
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All the Mathematics You Missed Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge‚ but few have such a background. This book will help students see the broad outline of mathematics and to fill in the gaps in their knowledge. The author explains the basic points and a few key results of the most important undergraduate topics in mathematics‚ emphasizing the intuitions behind the subject. The topics include linear
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psychometrics‚ and “basic structure” (Horst‚ 1963). The rescalings and centering‚ including their rationale‚ are well explained in Benzécri (1969)‚ Nishisato (1980)‚ Gifi (1981)‚ and Greenacre (1984). Those who are interested in the general framework of matrix approximation and reduction of dimensionality with positive definite row and column metrics are referred to Rao (1980). The delta method is a method that can be used for the derivation of asymptotic distributions and is particularly useful for the
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computations that are used in the PageRank algorithm. Some of the topics that we touch on include the following‚ but not limited to‚ are: linear algebra‚ node analysis‚ matrix theory‚ and numerical methods. But primarily this paper concerns itself with the use of the linear algebra involved in the computation of the Google matrix‚ which results in the Pagerank‚ which descibribes how important a page is. Importance is placed on the intuition of all related mathematical topics involved in the algorithm
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Introduction to Matlab: Application to Electrical Engineering Houssem Rafik El Hana Bouchekara Umm El Qura University (version 1‚ Februray 2011) 1 Contents 1 CHAPTER 1 ............................................................................................................................................ 7 1.1 TUTORIAL LESSONS 1 ................................................................................................................................ 7 1.1.1 1.2 STARTING AND QUITTING
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Exercise 3.1 Question 1: In the matrix ‚ write: (i) The order of the matrix (ii) The number of elements‚ (iii) Write the elements a13‚ a21‚ a33‚ a24‚ a23 Answer (i) In the given matrix‚ the number of rows is 3 and the number of columns is 4. Therefore‚ the order of the matrix is 3 × 4. (ii) Since the order of the matrix is 3 × 4‚ there are 3 × 4 = 12 elements in it. (iii) a13 = 19‚ a21 = 35‚ a33 = −5‚ a24 = 12‚ a23 = Question 2: If a matrix has 24 elements‚ what are the possible
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A SAMPLE RESEARCH PAPER/THESIS/DISSERTATION ON ASPECTS OF ELEMENTARY LINEARY ALGEBRA by James Smith B.S.‚ Southern Illinois University‚ 2010 A Research Paper/Thesis/Dissertation Submitted in Partial Fulfillment of the Requirements for the Master of Science Degree Department of Mathematics in the Graduate School Southern Illinois University Carbondale July‚ 2006 (Please replace Name and Year with your information and delete all instructions) Copyright by NAME‚ YEAR All Rights Reserved
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Simulation Modelling Practice and Theory 18 (2010) 712–731 Contents lists available at ScienceDirect Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat Singularity-free dynamic equations of vehicle–manipulator systems Pål J. From a‚*‚ Vincent Duindam b‚ Kristin Y. Pettersen a‚ Jan T. Gravdahl a‚ Shankar Sastry b a b Department of Engineering Cybernetics‚ Norwegian University of Science and Technology‚ Norway Department of EECS‚ University of California
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