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The determinant | Chapter 6, Essence of linear algebra

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Further reading 1

What does a matrix do, and which outputs can disappear? →Read a column as an arrow, then a matrix as an action on that arrow. Solving an equation becomes a question about reachable targets, giving collapse, eigenvectors and rotations a geometric interpretation.This video helps answer · Which equations survive a collapse in dimension?

Caption notes

The determinant measures signed area or volume scaling. Zero signals collapse into a lower dimension, and composing transformations multiplies their scale factors.

Original passages · 4
the factor by which a linear transformation changes any area
The determinant | Chapter 6, Essence of linear algebra · ▶ 2:28–2:37
A determinant of 0 would mean that all of space is squished onto something with 0 volume
The determinant | Chapter 6, Essence of linear algebra · ▶ 6:32–6:42
whenever the orientation of space is inverted, the determinant will be negative
The determinant | Chapter 6, Essence of linear algebra · ▶ 4:32–4:36
the same as the product of the determinants of the original two matrices
The determinant | Chapter 6, Essence of linear algebra · ▶ 9:20–9:30

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