I made a visualization of cofactor expansion for a 3×3 determinant.

The idea is to start with the usual interpretation of det(A) as signed volume, then show each cofactor term as:

• one coordinate projection of the expansion column

• one projected 2×2 minor in the orthogonal coordinate plane

So instead of treating

det(A) = a₁₁M₁₁ − a₂₁M₂₁ + a₃₁M₃₁

as only a symbolic rule, the goal is to make the three terms look like signed volume pieces.

The image shows the three terms for one example matrix, including the “same sign / negated sign” behavior of the cofactor signs.

Full explanation, including determinant sign:

https://www.graphmath.com/la/determinant/determinant-sign.html

I would be interested in feedback on whether the geometric interpretation is clear

I am primarily a visual learner and sycamore.to has been great to help me understand complex math concepts visually.

Hi guys,

Just wanted to say thank you for all the positive feedback from my first post about Linear Algebra Visualizer.

Especially from u/LongjumpingEar7568 and u/Ron-Erez who suggested adding the eigenvectors and values. This is now complete and I’m excited to share it with you guys in this community.

This update includes:

- Explore eigenvectors and eigenvalues visually

- Polygon presets

- Enter any 2x2 matrix

Thanks for your supports and let me know of any feedback in the comments please :)

Available on the platforms below:

Mac: https://apps.apple.com/gb/app/linear-algebra-visualizer/id6763524968

Linear Algebra Visualizer

iOS/iPad: https://apps.apple.com/us/app/linear-algebra-visualizer/id6763524968

Web: https://sockerjam.github.io/LinearAlgebraVisualizerWeb/ (Eigenvectors and values coming soon!)

This content is not intended for rigorous, proof-oriented linear algebra as practiced in mathematics departments.

Rather, it focuses on applied linear algebra suitable for immediate implementation in engineering and applied sciences.

The discussion primarily addresses the derivation of inverse matrices through Gauss-Jordan elimination and the adjugate matrix method.

I hope you find this useful for your work.

Quantum Physics Series

Video 1 of 6: Quantum Electrodynamics visualization using Feynman Diagrams

Author: Mugambi Ndwiga
In: www.instagram.com/craftsandengineering

This animation visualizes the fundamental interactions of Quantum Electrodynamics (QED) using Feynman diagram conventions. QED is the relativistic quantum field theory of electrodynamics, describing how light and matter interact.

Visualized Phenomena

The animation cycles through six key physical processes:

1. Compton Scattering: A photon hits an electron, resulting in an energy shift and change in direction.
2. Electron-Positron Annihilation: An electron and its antiparticle (positron) collide to produce high-energy photons ().
3. Pair Production: A high-energy photon interacts with the electric field of an atomic nucleus to create an electron-positron pair.
4. Bremsstrahlung (Braking Radiation): A charged particle (electron) is deflected by a nucleus and radiates energy as a photon.
5. Møller Scattering: The interaction and repulsion between two electrons via the exchange of a virtual photon.
6. Vacuum Polarization: A process where a photon temporarily fluctuates into a virtual electron-positron pair, affecting the vacuum's permittivity.

For code and more click Mathematical-video-animations-and-visualization/QED_Feynman_Diagrams_Animations.ipynb at main · zombimann/Mathematical-video-animations-and-visualization