Search for a tool
Change of Basis Matrix

Tool for calculating a change of basis matrix based on a homothety or rotation in a vector space and coordinate change calculations.

Results

Change of Basis 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!


Thanks to your feedback and relevant comments, dCode has developped the best Change of Basis Matrix tool, so feel free to write! Thank you !

Change of Basis Matrix

Sponsored ads

Change of Basis Equations Calculator

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

Rotation Matrix Calculator

From rotation data in 3D





From 2 vectors (any dimension)


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

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

Homothety Matrix Calculator



Tool for calculating a change of basis matrix based on a homothety or rotation in a vector space and coordinate change calculations.

Answers to Questions

How to calculate change of basis equations?

From a transformation matrix $ P $ (also called base change of basis matrix), any vector $ v $ then becomes the vector $ v' $ in the new base by the computation (dot / multiplication">matrix product) $$ v' = P.v $$

Example: $ \begin{pmatrix} v_1' \\ v_2' \end{pmatrix} = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} . \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} $

How to calculate a rotation matrix?

From a rotation angle $ \alpha $ (trigonometric direction) and an axis, the rotation matrix is written as (rotation around the axis $ z $) $$ \begin {pmatrix} \cos \alpha & - \sin \alpha & 0 \\ \sin \alpha \cos \alpha & 0 \\ 0 & 0 & 1 \ \end{pmatrix} $$

From 2 vectors (the original and the destination one), it is possible to generate an equation system to solve to find the values of $ \alpha $ and the axis.

How to calculate an homothety matrix?

From the value of the scaling factor $ k $ (homothety assumed to be uniform throughout the vector space of size $ n $), the passing matrix is given by the formula $$ k.I_n $$ (with $ I_n $ the identity matrix).

Source code

dCode retains ownership of the source code of the script Change of Basis Matrix online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Change of Basis Matrix script for offline use on PC, iPhone or Android, ask for price quote on contact page !

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developped the best Change of Basis Matrix tool, so feel free to write! Thank you !


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