The beauty and utility of linear algebra, courtesy of the new ChatGPT image model (or: how the same few ideas and methods apply to just about any field in endlessly fascinating ways, including AI!).

No other subject in math has more practical explanatory bang for the buck.

Prompts used:

Optimal visual depiction of using linear algebra to solve the optimal scarce allocation problem in economics and how and why the approach works in a realistic and concrete example, providing excellent visual intuition and motivation; beautiful and elegant appearance.

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Optimal visual depiction of using linear algebra and eigen-decomposition to model the stresses and forces in a system of steel trusses and how and why the approach works in a realistic and concrete example, providing excellent visual intuition and motivation; beautiful and elegant appearance.

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Optimal visual depiction of using linear algebra and eigen-decomposition to model the acoustic performance of a specific design for an auditorium space and how and why the approach works in a realistic and concrete example, providing excellent visual intuition and motivation; beautiful and elegant appearance.

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First, this:

Optimal visual depiction of Rank-Nullity theorem from linear algebra) and how and why it it’s true in various scenarios, providing excellent visual intuition and motivation; beautiful and elegant appearance.

Followed by this (pictured):

Cool, now make another one all about the practical applications of the theorem