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# Psycholinguistics PSY886

WSU

GPA 3.86

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This 12 page Class Notes was uploaded by Meggie Sauer on Thursday October 29, 2015. The Class Notes belongs to PSY886 at Wright State University taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/231119/psy886-wright-state-university in Psychlogy at Wright State University.

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Date Created: 10/29/15

Linear algebra 0 Elements gtScalars vectors matrices 0 Operations gtAddition amp subtraction vector matrix gtMultiplication scalar vector matrix gtDivision scalar matrix 0 Applications gtSignal processing others Scalars amp Vectors o Scalar fancy word for a number gteg 314159 or 42 gtScalar can be integer real or complex 0 Vector a collection of numbers gtage height weight or x y 2 roll pitch yaw gtWhy bother o Compact notation p e x y 2 roll piton yaw e i tneitn element eg in above p2y o Ease ot manipulation amples later Visualize a vector Y weight xiv l abelle Visualize a vector weiqu lab 5 o m sea AKg height Vectors 0 Row vector xx1 x2 x X1 X2 0 Column vector x M Xn o The transpose operator gtl1 xx1 X2 then xT l Operations Scalar multiplication 0 Vector multiplied by scalar gtMultiply each vector element by the scalar ax X1 ax o Scalar multiplication increases length of vector 0 If the scalar is negative also reverses direction of the vector Scalar multiplication axay Y Addition of vectors 0 EIement by element gt80 yy1gtlt1 y2gtlt2 yngtltn gtAssociative commutative gtAdd two likeshape vectors row amp row Dimensionz y Xty y X Dimension 1 Xi Y1 Linear combinations 0 Linear combinations of vectors gtExample ul cm czvz Linear independence 0 Set of all linear combinations of a set of vectors is the linear space spanned by the set 0 A set of vectors is linearly independent if none of the vectors in the set can be written as a linear combination of the other members of the set lnner product 0 Also called dot product gt xoy X1y1 X2y2 Xnyn 0 Maps two vectors to a m 0 Length also called m gt llxll is the length of the vector gt Note IIaxIIIaI IIxII Angle between two vectors 0 Defined using inner product gt 0056 u ll l llyll Example of compact notation 0 Set of data xgtlt1gtltquot yy1yquot 0 Correlation coefficient K 2 xkyk k1 n 2 k p quot 2 M M lg lg Basis vectors A basis for Vis a set of vectors Bin Vthat span V Vectorsin Bare lineary independent so any v in Vcan be written as a linear combination of vectors in B Orthogonal bases gt simple combinations gt Orthogonal ifu v 0 as cos Usual basis of infinitely many for F13 is gt B 100T 010T 001T gt coefficients of v using Bare coordinates Projections of vectors 0 Projection of v onto w gtIn 2 dimensions x v cos 6 or in higher Z dimensions is v w v w gtltllVlli llVllllWll ll ll V Projection onto basis Matrices o Matrices are arrays of numbers gtConvenient compact notation mtt m12 mti gteg M quot 21 quot 22 quot 23 o Are ogerators mapping between vector spaces eg change of basis or coordinates Matrices 0 Some special names gtSguare has same number of rows and columns gtDiagona has nonzero elements only on diagonal mapping vector space Ioi gtSymmetric is square with M1 MN if elements are all 1 call it I identity matrix Iself Matrix operations vectors gtCan multiply matrix by scalar gtCan add conforming matrices same rows columns 0 Multiply vector by matrix gt uWV U1 W11W12W13 Us W31 W32 W33 o If one considers a matrix as a set of Matrix multiplication 0 Can concatenate mappings gt If we have u Wu and v M2 then u WMz P2 0 W must have same number of rows as M has columns so multiplying an rxs matrix by sxtmatnx gives an rxtmatrix gtAssociative distributive but Lot commutative Inner and outer product 0 Inner product Maps two vectors to a scalar u v1v2 v3u2 a Us vectors toa vyu1 vyu2 vyua gt vuT v2u1u2 u3 v2u1v2u2 v2ua M V3 gtvu vTu 0 Outer product Maps two matrix v2u1 vau2 vaua Matrix inverse o The inverse of M is that matrix which when multiplied by M gives the identity matrix gtMMquot MquotM 0 Use the inverse forthe solution to n simultaneous linear equations gtlf y Ax then x Aquot y o M391 may not exist then M is singular Eigenvectors amp eigenvalues Matrix mapping u Wv takes domain V to range U Generally elements in Vare changed in length and direction Elements that are changed in length only are called eigenvectors of W gt WV 7 v then v is an eigenveotor of W with W 7 W can have more than one eigenvector they form a basis for the column space of W Psy886 Numerical Models RH Gilkey Course OVerV1eW Compromise between breadth not depth Topics 7 DSP r Neural Nets 7 Markov Models 7 Genetic algorithms 7 Matlab Tuesday vs Thursday Ordering Readings Evaluation Model A model is a simplification of another entity which can be a physical thing or another model The model contains exactly those characteristics and properties of the modeled entity which are relevant for a given task Theory A set of related statements that explains a variety of occurrences A tentative explanation for a phenomenon or set of phenomenon An internally consistent system that summarizes the data from the past and can be used to provide predictions to be tested in the future A model with coordinating operational definitions A logically organized set of propositions claims statements assertions that serves to define events concepts describe relationships among these events and explain the occurrence of these events Often we will construct a Model vs Theory Theories are intended to be general widely applica e model with a number of idealizations and assum io s 7 It is esier to work with such models than general systems 7 The model appues only to restriaed considerations Why Models Summarize data Explain data Generate predictions Guide applications Solve problems Types of models Descriptive Analogical Physical Quantitative Quantitative Models Analytic Closed form solutions Numerical Computational Models vs approaches Why use numerical approaches No closediforrn solution Not smart enough to derive a closed form solution The closediforrn is difficult to work with The closediforrn solution has parameters that must be fit to the data

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