Linear algebra and probability for computer science applications /
"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 grap...
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| Format: | eBook |
| Language: | English |
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Boca Raton, FL :
CRC Press,
©2012.
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| Series: | An A K Peters Book
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| Online Access: | Connect to the full text of this electronic book |
Table of 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