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