﻿ Matrix-Math© by Nova Software Innovation + Implementation℠

## Matrix Algebra Made Fast and Easy

### Including Dirac, Pauli and Gell-Mann matrices

#### If you work with matrices extensively this tool is for you.

• Work at your own convience directly on your own machine,
anywhere, anytime - no Internet connection needed.
• Blazingly fast, even on small portable PC's and tablets.
• Ultra-simple, intuitive math-like syntax
• Group related matrix work into one file.
• Include comments and scalar math too.
• Swift, effortless editing and recomputation
• Ideal for linear algebra students and teachers.
• Used by Nova Software, Inc. in its own physics research "Beyond the Standard Model"
• Completely free.

Download the zip file and unzip it to install it.

Totally self-contained, for any MSWindows host computer*. In a command window in the unzip folder type:

`matrix-math  HOW_TO_USE_M-M.nbk `
That file then shows you useful examples to jump start your use of Matrix-Math.
Get support via the 'message us' button on the support page.

• Free form input simplifies and speeds data entry.
• Includes all common matrix operations and more.
• Handles rational, real and complex numbers and symbolic expressions.
• Special features for Physics and Lie Algebra investigations:
• Dirac gamma matrices,
• Pauli matrices and su(2) IRR's,
• Gell-Mann matrices and su(3) IRR's.
• Output files can be formatted for publication.
• Complete documentation and test suites included.

## Matrix-Math© in Depth

Matrix-Math has been specifically written for ease-of-use, flexability, and versatility, while having speed, power, and a wealth of advanced features. It reads a plain text notebook to perform any sequence of matrix, vector, number and scalar operations. Results are written either to a separate plain text output notebook or back to the input notebook (the default) at the user's option.

Input Notebooks contain the user's descriptive and explanatory information interspersed with the commands that perform the calculations. The command expressions follow common math syntax for the operations they perform, so require hardly any learning effort. They cover the full range of matrix operations commonly required as well as many more advanced ones rarely seen in a program such as this. The commands handle all eligible types of variables appropriately and interchangeably internally, saving the user from managing fussy details better handled programatically.

Input Notebooks are free format, allowing a project to be structured any way desired. The quick startup and ease-of-use features make Matrix-Math ideal for students, new and occasional users, while its notebook method makes it indispensible for frequent users of matrix algebra such as those teaching linear algebra. In addition its speed of operation and advanced physics and Lie-algebra-representations-oriented features make it well-suited for advanced math and physics workers and researchers.

Matrix-Math overlaps in some areas with some well-known computer algebra systems. It differs from the high-end ones by being free, by the simplicity and generality of its expressons, by its flexible formatting, and by its special features. It differs from the free ones by being much lighter weight and faster, by its simpler, more general syntax and flexible formatting, and by its wider range of matrix operations.

Matrix-Math's output notebook follows the order of the input notebook. Results of the command operations appear where they occur, marked by an optional vertical bar in the first column, making for a convenient automatic record of the reasoning, logic and sequence of steps of a matrix project of any magnitude. Output notebooks are ideal for capturing and submitting course work and problem sets involving matrices as well as for accurately documenting more advanced investigations.

Input notebooks are written with any plain text Unicode UTF-8-enabled text editor and given the .nbk extension. Each notebook run normally completes in a few seconds or less, so developing a notebook solution is essentially interactive. Extensive error trapping and reporting and a debug output option are provided for quick, easy troubleshooting.

Matrix-Math works with numeric and symbolic input: Integers, decimals, rationals and floating point numbers, as well as a very general form of symbolic expression and complex numbers. Numeric results are given to the full single-precision capability of the host computer in the appropriate format. It does not currently feature graphing nor emphasize solving linear equations since those capabilities are readily available elsewhere.

Download the zip file and unzip it to install it.

Syntax Overview:
• All operations to be performed are enclosed in a pair of angle brackets thus:
`<< A = B * C >>`
• Identifiers (variable names), equal signs and operators in those expressions are separated by one or more spaces.
• Names may be up to 251 characters long and use only alphanumeric and '_' characters.
• Numeric values are limited by the size of a single precision floating point number on the host system.
• Integers which exceed the size of a native integer on the host system overflow automatically to floating point with a loss of precision.
• Symbolic values are limited only by available memory.
• All non-command text in the input notebook is passed thru as-is to the output notebook.
• Define a matrix:
```<< A =
1.0  .2   .03
4   .4e5  0.6
7.  1E-8   9
>>```
• Define a matrix with a leading coefficient:
```<< B = 5 *
1 2 3
4 5 6
7 8 9
>>```
• Determinant of a defined matrix:
`<< C = det B >>`
• Define a left-diagonal matrix:
`<< D = diag 1 2 3 4 5 >>`
• Other operations on matrices, vectors and scalars include multiply, add, subtract, inverse, transpose, adjoint, integer power, compare, trace, matrix exponentiation, matrix direct sum, matrix tensor product, matrix commutators and anti-commutators, along with right-multiply versions of these where different.
• Rectangular matrices are handled where applicable.
• The Pauli, Gell-Mann and Dirac gamma matrices are built in.
• The fundamental and adjoint irreducible representations of su(2) and su(3) Lie algebras are built-in.
• Find eigenvalues and eigenvectors of square matrices.
• Test a matrix for unitarity or identity.
• Optional limits for rounding numeric results.
• Complete documentation is provided in the zip file.
• The complete suite of tests used for product development is included.
• Matrix differentiation and some related aspects of diffential geometry and topological groups are planned.
• Other features that may be added later.
• Double precision results
• Sparse matrices
• Graphing
• Optimized calculation methods for large dense numeric matrices.

Download the zip file and unzip it to install it.

Please let us know how it works for you!
Cite it in your research results, course notes or texts as Matrix-Math©, matrix-math.net, Nova Software, Inc., 2022
* Contact us for a Linux version. Not available on MacOS, or Android.