@EricLengyel In the absence of exterior algebra, you can also have students discuss why symmetry, bilinearity, and positivity are natural geometric properties for any inner product.

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• URL: https://x.com/keenanisalive/status/1229351518614249472
• Author: Keenan Crane (@keenanisalive)
• Posted: 2020-02-17 10:26:56

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1/ @keenanisalive

@EricLengyel

In the absence of exterior algebra, you can also have students discuss why symmetry, bilinearity, and positivity are natural geometric properties for any inner product. Then show that the Euclidean dot product is the only one invariant to (Euclidean) rigid motions, up to scale.

2/ @AntoPatriarca

@keenanisalive @EricLengyel

This was shown to me in my first linear algebra course at college. I would argue GA does not make any of this easier, it just change what is considered as a basic definition and what is instead derived from them.

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