Linear algebra and probability for computer science applications. (©2012)

• Record Type: Book
• Further Information: Note: Ernest Davis.
• Other Names: Davis, Ernest
• 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
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2012
• Copyright Date: 2012
• Extent: 1 online resource (xviii, 413 pages), illustrations
• Subjects: 004.0151; Computer science -- Mathematics; Algebras, Linear; Probabilities; Algebras, Linear; Computer science -- Mathematics; Probabilities; Electronic books
• Languages: English
• ISBNs: 9781466501591; 1466501596
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.