26 lines
873 B
Text
26 lines
873 B
Text
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#import "@preview/unequivocal-ams:0.1.1": ams-article, theorem, proof
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#show: ams-article.with(
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title: [Week 2],
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authors: (
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(
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name: "Youwen Wu",
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organization: [University of California, Santa Barbara],
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email: "youwen@ucsb.edu",
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url: "https://youwen.dev",
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),
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),
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bibliography: bibliography("refs.bib"),
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)
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= Vectors, linear combinations, spans, matrix-vector product.
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- Consider a whole new way of looking at linear systems
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- Add vectors entrywise, head to tail
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- Multiply vectors via scaling
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- A more flexible way to draw a line. For a line through point $p$, in direction $arrow(d)$, use $arrow(p) + t arrow(d), t in RR$. Intuition: Add a vector $arrow(p)$ pointing to point $p$ and compose a vector pointing in the intended direction $arrow(d)$ head to tail.
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A linear combination is
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$ arrow(y) = sum_(k=1)^n alpha_n arrow(v)_n $
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