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Highlights from
Introduction to Linear Algebra

  • BASIS(A)BASIS Basis for the column space.
  • addvec(v,w)ADDVEC Illustrate the sum v + w of 2-dimensional vectors.
  • atimesv(a,v)atimesv displays a two-dimensional
  • cofactor(A,i,j)COFACTOR Cofactors and the cofactor matrix.
  • cosineCOSINE Illustrates cosine formula and dot products.
  • cramer(A,b)CRAMER Solve linear system by Cramer's Rule.
  • determ(A)DETERM Matrix determinant from PLU.
  • eigen(A)EIGEN Describe eigenvalues and eigenvectors.
  • eigen2(a)EIGEN2 Two by two eigenvalues and eigenvectors.
  • fastfour(x)FASTFOUR Fast Fourier Transform.
  • findpiv(A,k,p,tol)FINDPIV Used by PLU to find a pivot for Gaussian elimination.
  • grams(A)GRAMS Gram-Schmidt orthogonalization.
  • inverse(A)INVERT Matrix inverse by Gauss Jordan elimination.
  • linefit(t,b)LINEFIT Plot the least squares fit by a line.
  • linprog(A,b,c,k,maxit,tol)LINPROG This code uses the revised simplex method to solve the linear
  • lsq(A,b)LSQ Least squares.
  • null(A)NULL Nullspace of a matrix
  • permdet(p)PERMDET Determinant of a permutation.
  • plot2d(X)PLOT2D Two dimensional plot.
  • plu(A)PLU Pivoting, rectangular, LU factorization.
  • poly2str(c,x)POLY2STR Convert a polynomial coefficient vector to a string.
  • power(A,v,n)POWER Execute the power method on a 2 by 2 matrix A
  • projmat(A)PROJMAT Projection matrix onto the column space.
  • randperm(n)RANDPERM Random permutation.
  • rats(A)RATS Print in "rational" form.
  • ref(A)REF Reduced Row Echelon Form.
  • signperm(p)SIGNPERM Sign of a permutation.
  • slu(A)SLU Simple, square, LU factorization.
  • slv(A,b)SLV Simple linear equation solver.
  • solve(A,b)SOLVE Particular solution to a system of simultaneous linear equations.
  • splu(A)SPLU Square LU factorization with row exchanges.
  • splv(A,b)SPLV The solution to a square, invertible system.
  • Contents.mStrang Linear Algebra Toolbox
  • Readme.mINTRODUCTION TO LINEAR ALGEBRA TOOLBOX
  • expage35.mEXPAGE35 Tutorial of Markov programming exercise.
  • expage36.mMARKOV2 Tutorial of Markov programming exercise.
  • expower.mEXPOWER demonstrates the power method of finding the dominant eigenvalue
  • fourier.mThis code starts by creating the Fourier matrix.
  • hand.m"Hand" data set for use with plot2d.
  • house.m"House" data set: The 2 by 12 matrix for the coordinates of the
  • movies.mMATLAB has a "movie" to show how elimination reaches the
  • sixpack.mSIXPACK shows the six orderings for the loops in matrix multiplication.
  • xbasis.mA basis consists of independent vectors whose combinations produce the whole
  • xcofactor.m
  • xcramer.mCramer's Rule solves Ax = b by determinants. The j-th component of the
  • xdeterm.mStart with the determinant of a pascal matrix that has the pascal
  • xeigen.mThis code uses the power of MATLAB's eig program to find eigenvalues
  • xeigen2.mThis code gives the eigenvalues and eigenvectors of a 2 by 2 matrix.
  • xfindpiv.mThis is about the function FINDPIV, which is used by the PLU function
  • xgrams.mThe Gram-Schmidt process starts with independent vectors in the columns of A
  • xinverse.mThe inverse of A is here computed by Gauss-Jordan elimination on [A I].
  • xlinefit.mThe linefit program draws the closest (least squares) line to a set of points
  • xlsq.m
  • xnull.mThe nullspace matrix N contains the "special solutions" to Ax=0.
  • xpermdet.mThe determinant of a permutation matrix is always 1 or -1. This is also
  • xplot2d.mThe front cover of the book shows "houses" that were drawn using plot2d.
  • xplu.mEvery matrix allows the factorization PA = LU. If A is square and invertible
  • xprojmat.mStart with random matrices and project onto their column spaces.
  • xrandperm.m
  • xrats.mThis code gives the output in terms of FRACTIONS instead of decimals.
  • xref.m% For every matrix A, the reduced echelon form R has all pivots = 1 and zeros
  • xsignperm.mA permutation can be given two ways - as a series of numbers p or a matrix P.
  • xslu.m
  • xslv.mThe solve program slv uses slu to factor A into L*U. The matrix A must
  • xsolve.mChoose a square matrix with dependent columns u, v, w.
  • xsplu.mChoose a matrix with zeros on its diagonal:
  • xsplv.m
  • zeroone.mThis program creates matrices with 0's and 1's at random. It counts the
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Introduction to Linear Algebra

by

 

20 Aug 2002 (Updated )

Companion Software

atimesv(a,v)
function atimesv(a,v)
%       atimesv  displays a two-dimensional
%       plot of the scalar-vector product a*v,
%       where a is a real scalar and v is a two
%       dimensional real vector.
%
%       This function displays a plot of a*v
%       following the illustration of Figure 1.1 in G. Strang,
%       "Introduction to Linear Algebra."

% Written by T. A. Bryan on 2 June 1993

x=a*v;

hold off
clg
plot([0 v(1)],[0,v(2)],':',...
    [0 x(1)],[0,x(2)],'-')
hold on
text(v(1),v(2),'v')
text(x(1),x(2),[num2str(a) '*v'])

hold off


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