Tool for calculating a transition matrix (change of basis) based on a homothety or rotation in a vector space and coordinate change calculations.
Transition Matrix - dCode
Tag(s) : Matrix
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Transition Matrix
Transition Equations Calculator
Rotation Matrix Calculator
Homothety Matrix Calculator
Answers to Questions (FAQ)
What is a transition matrix? (Definition)
The transition matrix is the matrix allowing a calculation of change of coordinates according to a homothety or a rotation in a vector space.
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: [v′1v′2]=[1234].[v1v2]
How to calculate a rotation matrix?
From a rotation angle α (trigonometric direction) and an axis, the rotation matrix is written as (rotation around the axis z) [cosα−sinα0sinαcosα0001 ]
From 2 vectors (the original and the destination one), it is possible to generate an equation system to solve to find the values of α and the axis.
How to calculate a 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.In (with In the identity matrix).
Source code
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Transition Matrix on dCode.fr [online website], retrieved on 2025-03-26,
