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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. The application currently supports: XY line and scatter plots 2D contour plots Interactive 3D contour surfaces Multi-panel figure composition CSV, TSV, and text data import PNG and vector PDF export Versioned .splot project files Stable and invite-protected Beta update channels ScientificPlotter currently requires an Apple Silicon Mac running macOS 13 or later. ...

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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