Search for a tool
Hermite Normal Form Matrix

Tool for calculating the Hermite normal form (by reducing a matrix to its row echelon form) from a matrix M (with coefficients in Z) the computation yields 2 matrices H and U such that $ H = U . M $.

Results

Hermite Normal Form Matrix -

Tag(s) : Matrix

Share
Share
dCode and you

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Please, check our community Discord for help requests!


Thanks to your feedback and relevant comments, dCode has developped the best Hermite Normal Form Matrix tool, so feel free to write! Thank you !

Hermite Normal Form Matrix

Hermite Form Calculator

Loading...
(if this message do not disappear, try to refresh this page)

Tool for calculating the Hermite normal form (by reducing a matrix to its row echelon form) from a matrix M (with coefficients in Z) the computation yields 2 matrices H and U such that $ H = U . M $.

Answers to Questions

How to calculated the Hermite decomposition?

A matrix $ M $ of size $ n \times m $ with integer coefficients (natural or relative) has a Hermite decomposition if there exists a triangular matrix $ H $ and a unimodular matrix $ U $ such that $ H = U. M $. Reminder: An upper triangular matrix $ H $ is such that $ H_ {i, j} = 0 $ for $ i> j $ and a unimodular matrix is an invertible square matrix with integer coefficients whose determinant is $ \pm 1 $.

Example: $$ M = \begin{bmatrix} 3 & 2 & 1 \\ 0 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix} \Rightarrow H = \begin{bmatrix} 0 & -1 & 1 \\ 0 & 1 & 0 \\ -1 & -1 & 3 \end{bmatrix}, U = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 2 \end{bmatrix} $$

There are two forms for the Hermite matrix, an upper triangular matrix such that $ H = UM $ (also called Hermite's normal form row style) is a lower triangular matrix such that $ H = MU $ ( also called Hermite normal form column style)

dCode uses the LLL algorithm (Lenstra-Lenstra-Lovász) to calculate the Hermite decomposition (the calculation by hand is not recommended)

What is the Hermite Normal Form?

A normal Hermite-shaped matrix is the triangular scaled matrix $ H $ calculated by the Hermite decomposition (above) via reduction to row echelon form of the matrix.

Source code

dCode retains ownership of the online 'Hermite Normal Form Matrix' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Hermite Normal Form Matrix download for offline use on PC, tablet, iPhone or Android !

Need Help ?

Please, check our community Discord for help requests!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developped the best Hermite Normal Form Matrix tool, so feel free to write! Thank you !


Source : https://www.dcode.fr/matrix-hermite
© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback