**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

**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
**R**^{n} - Div - elementary row operation
- Dot - dot product of two vectors in
**R**^{n}

- 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
**R**^{n} - 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
**R**^{n}

- 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