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e^(iπ) in 3.14 minutes, using dynamics | DE5

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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 · Why does an exponential trace a circle?

Caption notes

Multiplication by i turns a position vector through a right angle. If velocity always equals that turned vector, a point starting at one travels around the unit circle rather than growing radially.

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Original passages · 2
the velocity at that time will be a 90 degree rotation of that position.
e^(iπ) in 3.14 minutes, using dynamics | DE5 · ▶ 2:21–2:33
If e to the t describes your position on a number line as a function of time, then you start at the number 1, and what this equation is saying is your velocity, the derivative of position, is always equal to that position.
e^(iπ) in 3.14 minutes, using dynamics | DE5 · ▶ 0:20–0:32

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