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ScientificPlotter is a native macOS application for scientific data visualization. I started this project because I wanted a plotting tool that feels at home on macOS while still providing the features needed for research and numerical work. The goal is not to replace every established plotting package, but to offer a focused and responsive desktop application for exploring data, preparing figures, and exporting publication-ready graphics. Main features include: XY line, scatter, and analytical function plotting 2D contours and interactive 3D surfaces 2D and 3D finite-element visualization Data import and reusable analysis workflows 3D scene composition and 2D diagrams Multi-panel figures with custom layouts, legends, and zoom insets PNG, vector PDF, and scientific data export Versioned .splot projects with checkpoints Stable and invite-protected Beta update channels ScientificPlotter 2.0.0 requires an Apple Silicon Mac running macOS 27 or later. This release has been qualified on an M4 Pro Mac. ...

Derivative of a matrix inverse The derivative of a matrix inverse $\boldsymbol{A}^{-1}$ with respect to $\boldsymbol{A}$ is a 4th order tensor. Since $\dfrac{\partial}{\partial \boldsymbol{A}} \left( \boldsymbol{A}^{-1} \boldsymbol{A} \right) = 0$, $\dfrac{\partial \boldsymbol{A}^{-1}}{\partial \boldsymbol{A}} = - \boldsymbol{A}^{-2}$, but deriving its counterpart based on Einstein notation is not so obvious. Owing to, $$ 0 = \frac{\partial \delta_{km}}{\partial A_{ij}} = \frac{\partial A_{kl}^{-1}}{\partial A_{ij}} A_{lm}+A_{kl}^{-1} \frac{\partial A_{lm}}{\partial A_{ij}} $$and $$ \frac{\partial A_{kn}^{-1}}{\partial A_{ij}} = \frac{\partial A_{kl}^{-1}}{\partial A_{ij}} A_{lm} A_{mn}^{-1} = - A_{kl}^{-1} \frac{\partial A_{lm}}{\partial A_{ij}} A_{mn}^{-1}, $$where ...

The Orthogonal Decomposition Theorem Let $V$ be a Hilbert space and $M\subset V$ a closed subspace of $V$. Then (i) $M^\bot$ is a closed subspace of $V$. (ii) $V$ can be represented as the direct sum of $M$ and its orthogonal complement $M^\bot$ $$ V=M\oplus M^\bot $$i.e., every vector $v\in V$ can be uniquely decomposed into two orthogonal vectors $\boldsymbol m$, $\boldsymbol n$, s.t. $$ \boldsymbol v=\boldsymbol m+\boldsymbol n, \boldsymbol m\in M,\boldsymbol n\in M^\bot $$COROLLARY Let $V$ be a Hilbert space and $M$ a vector subspace of $V$ . The following conditions are equivalent to each other (i) $M$ is closed. (ii) $(M^\bot)^\bot = M$. ...

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