Matlab Depot

## MATLAB DEPOT

#####
Feel free to download and use (at your own risk!)
any of the following matlab functions and
scripts. If you want to contribute some of your
M-files or have other suggestions, please
e-mail.

This page is linked from the portal
Mathtools.net.

Last updated: Apil 9, 2014

To download, hold the SHIFT key down when
you click on the filenames.

dig.m

Finds the strongly connected components of the directed graph
of a matrix.

frob.m

Uses dig.m to find the Frobenius normal form of a matrix.

ppt.m

Finds the Principal Pivot Transform of a matrix relative to a
principal submatrix.
See Principal Pivot Transforms: Properties and
Applications.

digit.m

Given a positive integer k in decimal form, it generates vectors d, b,
whose entries are the digits of the decimal and binary representations
of k, respectively.

hmat.m

Finds, if possible, a diagonal matrix
D such that AD is strictly row diagonally dominant.
In other words, check if A is an H-matrix or not.
This is achieved using Algorithm H found in
An Iterative Criterion for H-matrices.

nr.m

Draws the (boundary of the) numerical range of a matrix.

ptest3.m

Checks if a (complex) matrix is P (i.e., if all its
principal minors are positive) or not. Uses a recursive algorithm
found in A Recursive Test
for P-matrices.
[ ptest3.m is an improvement upon the original
ptest.m which was designed to
test real matrices only and was much slower.]

shell.m

Draws the "shell" of an almost skew-symmetric matrix.
It needs spectrum.m.

An almost skew-symmetric matrix is a matrix whose
symmetric part has rank one. Its shell is a curve in the
complex plane that localizes the spectrum. This M-file
draws the shell and plots the eigenvalues. Such
matrices are studied in a recent paper by Panos Psarrakos,
Judi McDonald and myself. Request a
preprint.

rtour.m

Generates a "random" tournament matrix.

spectrum.m

Simple file to plot the spectrum of a matrix.

schurc.m

Finds a Schur complement.

Principal Minor Computation and Assignment

This is a page with links to (p)re-prints and Matlab source code related
(1) to the computation of all principal minors of a matrix and (2) to
the Principal Minor Assignment Problem.

envelope.m

Finds the Envelope of a matrix, which is a region in the complex plane that
contains the spectrum. See my work with Panos Psarrakos for the definition
and properties of the Envelope.

Some other useful M-files:

bidiag.m

fiedler.m

cjf2rjf.m

companc.m