Least Squares, Minimum Norm, Pseudo-Inverse Solutions
May 4, 2025
Preface For a system of linear "equations" (may not actually be equal) $$ Ax \backsimeq b $$ where $ A\in\mathbb{R}^{m \times n}, x\in \mathbb...
Rotation Dynamics, Magnus Series, and Implementation
Apr 20, 2025
Rotation Matrix Derivative, Exponential, Magnus Series As discussed in 2020@Huber and Welshman@2013 , the time derivative of a rotation matrix $R$ with an angular velocity $\omega$ is...
Eigen · Rotation Logarithm and Exponential
Apr 13, 2025
Rotation Matrix Logarithm and Exponential As discussed in Exponential and Logarithm in SO(3), SE(3), Quaternion Space, the formulas are as follows. $$ \log(R) = [\hat{\omega}]\theta $...
Eigen 101 · Aliasing, Function Arguments and Reference
Apr 5, 2025
Some brief notes for quick reference. Aliasing It occurs when the same matrix or array coefficients appear both sides of an assignment operator. In general when you multiply two matrices, Eigen assumes...
Python · Poetry Project Notes
Mar 22, 2025
Some brief notes for quick reference. Poetry project folder structure. Contents in pyproject.toml, a project setup example. It can be created manually or generated via poetry init, and updated by poetry...