The Linear Algebra with Applications Toolbox

by

Gareth Williams and Lisa Coulter, Stetson University

Programs (M-files) for MATLAB to accompany Linear Algebra with Applications

(download the Toolbox)

Use and modification guidelines:

These files may be downloaded and used with MATLAB. The user may modify these files for personal or class use as long as he/she acknowledges the above authors. Such modified files are not to be sold or distributed.

M-files:

• Add - elementary row operations
• Adj - adjoint of a matrix
• Affine - affine transformations of a unit square
• Angle - angle between two vectors (in degrees)

• Circle - circles in an inner product space
• Cminor - compute a minor of a matrix
• Cn - condition number and matrix statistics
• Compmap - composition of two mappings
• Cramer - Cramer's rule
• Cross - cross product of vectors

• Digraph - picture and information about a digraph
• Dist - distance between two points in Rⁿ
• Div - elementary row operation
• Dot - dot product of two vectors in Rⁿ

• Echtest - test random 3x3 matrices for REF

• Fern - fractal fern
• Frac - rational form for matrix elements

• Galg - pattern of algorithm in Gaussian elimination
• Gangle - angle between two vectors in an inner product space
• Gdist - distance between two points in an inner product space
• Gelim - Gaussian elimination
• Ginfo - statistics for Gaussian elimination
• Ginner - inner product of two vectors in an inner product space
• Gjalg - pattern of algorithm in G/J elimination
• Gjdet - determinant using G/J elimination
• Gjelim - Gauss/Jordan elimination
• Gjinfo - statistics for G/J elimination
• Gjpic - lines for G/J elimination
• Gjinv - matrix inverse using G/J elimination
• Gnorm - norm of a vector in an inner product space
• Gpic - lines for Gaussian elimination
• Gramschm - Gram/Schmidt orthogonalization
• Graph - graph of a polynomial function
• Gseidel - Gauss/Seidel method

• Jacobi - Jacobi method

• Leoinv - matrix inverse in the Leontief Model
• Leontief - economic predictions using the Leontief Model
• Lindep - check linear independence
• Lsq - computation and sketch of a least squares fit curve
• Lufact - LU decomposition of a matrix
• Lusolve - solution using Lufact

• Mag - magnitude of vector in Rⁿ
• Map - matrix mapping of unit square
• Markov - Markov chain model
• Minor - minors of a matrix
• Mult - elementary row operation

• Ops - number of arithmetic operations in matrix multiplication

• Perminv - inverse of a permutation
• Permprod - product of permutations
• Pic - function for drawing graphs
• Picture - graphs of lines
• Pivot - complete pivoting
• Pow - powers of a matrix
• Proj - vector projection in Rⁿ

• Sierp - Sierpinski triangle
• Siml - similarity transformation
• Simplex - the simplex method
• Space - a simulation of a space/time voyage
• Square - fractal square
• Swap - elementary row operation

• Tdot - triple scalar product
• Transf - elementary row operations
• Tree - fractal tree