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Linear algebra and probability for computer science applications

Author: Ernest Davis
Publisher: Boca Raton, FL : CRC Press, ©2012.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"Taking a computer scientist's point of view, this classroom-tested text gives an introduction to linear algebra and probability theory, including some basic aspects of statistics. It discusses examples of applications from a wide range of areas of computer science, including computer graphics, computer vision, robotics, natural language processing, web search, machine learning, statistical analysis, game playing,  Read more...
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Details

Document Type: Book
All Authors / Contributors: Ernest Davis
ISBN: 9781466501553 1466501553
OCLC Number: 748331587
Description: xviii, 413 p. : ill. ; 25 cm.
Contents: MATLAB Desk calculator operations Booleans Nonstandard numbers Loops and conditionals Script file Functions Variable scope and parameter passing I: Linear Algebra Vectors Definition of vectors Applications of vectors Basic operations on vectors Dot product Vectors in MATLAB: Basic operations Plotting vectors in MATLAB Vectors in other programming languages Matrices Definition of matrices Applications of matrices Simple operations on matrices Multiplying a matrix times a vector Linear transformation Systems of linear equations Matrix multiplication Vectors as matrices Algebraic properties of matrix multiplication Matrices in MATLAB Vector Spaces Subspaces Coordinates, bases, linear independence Orthogonal and orthonormal basis Operations on vector spaces Null space, image space, and rank Systems of linear equations Inverses Null space and Rank in MATLAB Vector spaces Linear independence and bases Sum of vector spaces Orthogonality Functions Linear transformations Inverses Systems of linear equations The general definition of vector spaces Algorithms Gaussian elimination: Examples Gaussian elimination: Discussion Computing a matrix inverse Inverse and systems of equations in MATLAB Ill-conditioned matrices Computational complexity Geometry Arrows Coordinate systems Simple geometric calculations Geometric transformations Change of Basis, DFT, and SVD Change of coordinate system The formula for basis change Confusion and how to avoid it Nongeometric change of basis Color graphics Discrete Fourier transform (Optional) Singular value decomposition Further properties of the SVD Applications of the SVD MATLAB II: Probability Probability The interpretations of probability theory Finite sample spaces Basic combinatorial formulas The axioms of probability theory Conditional probability The likelihood interpretation Relation between likelihood and sample space probability Bayes' law Independence Random variables Application: Naive Bayes' classification Numerical Random Variables Marginal distribution Expected value Decision theory Variance and standard deviation Random variables over infinite sets of integers Three important discrete distributions Continuous random variables Two important continuous distributions MATLAB Markov Models Stationary probability distribution PageRank and link analysis Hidden Markov models and the k-gram model Confidence Intervals The basic formula for confidence intervals Application: Evaluating a classifier Bayesian statistical inference (Optional) Confidence intervals in the frequentist viewpoint: (Optional) Hypothesis testing and statistical significance Statistical inference and ESP Monte Carlo Methods Finding area Generating distributions Counting Counting solutions to DNF (Optional) Sums, expected values, integrals Probabilistic problems Resampling Pseudo-random numbers Other probabilistic algorithms MATLAB Information and Entropy Information Entropy Conditional entropy and mutual information Coding Entropy of numeric and continuous random variables The principle of maximum entropy Statistical inference Maximum Likelihood Estimation Sampling Uniform distribution Gaussian distribution: Known variance Gaussian distribution: Unknown variance Least squares estimates Principal component analysis Applications of PCA References Notation Index
Responsibility: Ernest Davis.

Abstract:

"Taking a computer scientist's point of view, this classroom-tested text gives an introduction to linear algebra and probability theory, including some basic aspects of statistics. It discusses examples of applications from a wide range of areas of computer science, including computer graphics, computer vision, robotics, natural language processing, web search, machine learning, statistical analysis, game playing, graph theory, scientific computing, decision theory, coding, cryptography, network analysis, data compression, and signal processing. It includes an extensive discussion of MATLAB, and includes numerous MATLAB exercises and programming assignments"--
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