quartz/content/Obsidian Vault/LinearAlgebra1.md

cards-deck	date	tags
default_obsidian	2022-04-27

#math/linear_algebra

Dot Product

multiply each number in a vector by the one in the corresponding index in the other. then add it all up.

Length of vector

#card dot product with itself, square root. it's the pythagorean theorem.

||v||=\sqrt{v\cdot v}

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unit vector

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||cv|| = |c|\ ||v||

vector divided by its length, you get a vector of length 1 ^1651363913154

Distance:

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dist(u,w)=||u-w||

you are basically subtracting the vectors, and doing pythagorean to get the length of that resulting vector ^1651363193147

cauchy-schwartz

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|u\cdot w|\leq ||u||\ ||w||

basically, the dot product is always smaller than the two lengths multiplied ^1651363193158

triangle inequality

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||u+w||=||u||+||w||

the length of the added vectors is always smaller than the added lengths of the vectors. ^1651363193169

angles?

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cos\theta = \frac{uv}{||u||\ ||v||}=\frac{u}{||u||}\cdot \frac{v}{||v||}

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