Linear Algebra 19c: Illustration of Component Spaces by a Sum of Geometric Vectors

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I feel like this video could have come wayy sooner in the series. Nevertheless I'm glad it did eventually. I'm finally getting why you were so much against mixing geom. vectors and the standard grid in the beginning. It has been a challenge to stick around, as I've been first exposed to the "usual" way of teaching and something seemed off for a long time. Thanks!

Filifow
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just the video i needed to understand matrix representation of linear transformations.

m.o.cfitnessrolemodels
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How would the addition work in polar coordinates? Can you do it without introducing a background cartesian basis? Doing that seems like cheating. There also appears to be a difference between a basis and a coordinate system.

finweman
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very nice points. I just didn't get how did get b fro (f1, f2). I seam more likely that:
b=(1, eqr(2))^T

luisribeiro