Linear Algebra and Probability for Computer Science Applications (Hardcover)

MATLABDesk 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 vectorsBasic operations on vectorsDot productVectors in MATLAB: Basic operationsPlotting vectors in MATLABVectors 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 independenceOrthogonal and orthonormal basis Operations on vector spaces Null space, image space, and rank Systems of linear equations Inverses Null space and Rank in MATLABVector spaces Linear independence and bases Sum of vector spacesOrthogonality Functions Linear transformations Inverses Systems of linear equations The general definition of vector spaces Algorithms Gaussian elimination: Examples Gaussian elimination: DiscussionComputing a matrix inverse Inverse and systems of equations in MATLAB Ill-conditioned matrices Computational complexity Geometry Arrows Coordinate systems Simple geometric calculationsGeometric transformations Change of Basis, DFT, and SVD Change of coordinate systemThe formula for basis change Confusion and how to avoid it Nongeometric change of basis Color graphics Discrete Fourier transform (Optional)Singular value decompositionFurther properties of the SVDApplications of the SVDMATLAB II: Probability Probability The interpretations of probability theory Finite sample spaces Basic combinatorial formulas The axioms of probability theoryConditional probability The likelihood interpretation Relation between likelihood and sample space probability Bayes’ law IndependenceRandom variables Application: Naive Bayes’ classification Numerical Random Variables Marginal distribution Expected value Decision theoryVariance and standard deviation Random variables over infinite sets of integers Three important discrete distributionsContinuous random variables Two important continuous distributionsMATLAB Markov Models Stationary probability distribution PageRank and link analysisHidden 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 algorithmsMATLAB Information and Entropy Information Entropy Conditional entropy and mutual information Coding Entropy of numeric and continuous random variables The principle of maximum entropyStatistical 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