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An illustrated introduction to linear algebra

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Re: An illustrated introduction to linear algebra

#41

Post by airstrike »

dylan604 wrote: post #37

"Aside: Another solution for the above is 23 pennies. Or -4 nickels + 43 pennies." This is where the math nerds just can't help themselves, and I'm here for it. However, these things drive me crazy at the same time. You cannot have -4 nickels. In pure math with only x and y, sure those values can be negative. But when using real world examples using physical objects, no, you cannot have a negative nickel. Maybe you o…

Doesn't that help rule out that other solution in favor of the reasonable one?

Re: An illustrated introduction to linear algebra

#42

Post by coolandsmartrr »

Miserlou57 wrote: post #38

about 15 years ago I started an aggregator to accumulate/sort/filter the best instruction of various topics, kinda like Reddit for learning. This is such a perfect example of the kind of thing I hoped would filter to the top. Thinking about trying to redo it. Is there a use for this sort of thing in today's world?

Yeah, I like this kind of content too. Do you still have the aggregator available online?

Re: An illustrated introduction to linear algebra

#43

Post by egonschiele »

vonnik wrote: post #23

I really like this, and I think one way to make it even more clear would be to use other variable letters to represent breads and milks, because their x’s and y’s somehow morph into the x’s and y’s that represent carbs and protein in the graph.

Agreed, something about the variables is confusing, I need to think about what to change there!

Re: An illustrated introduction to linear algebra

#44

Post by emmelaich »

egonschiele wrote: post #13
dawnofdusk wrote: post #11

I really like the second part of the blogpost but starting with Gaussian elimination is a little "mysterious" for lack of a better word. It seems more logical to start with a problem ("how to solve linear equations?" "how to find intersections of lines?"), show its solution graphically, and then present the computational method or algorithm that provides this solution. Doing it backwards is a little like teaching the…

Author here – I think you're probably right. I wrote the Gaussian elimination section more as a recap, because I figured most readers have seen Gaussian elimination before, and I was keen to get to the rest of it. I'd love to hear if other folks had trouble with this section. Maybe I need to slow it down and explain it better.

To some, "Now we can add the two equations together to eliminate y: might need a little explanation.

The (an) answer is that since the LHS and RHS are equal, you can choose to add or subtract them to another equation and preserve equality.

If I remember correctly, substitution (isolating x or y) was introduced before this technique.

Re: An illustrated introduction to linear algebra

#45

Post by egonschiele »

oatsandsugar wrote: post #4

That's really intuitive, especially your description of column notation. Excited to read your other guides! Also, HT to your user name! Egon Schiele is one of my favorite artists! Loved seeing his works at the Neue in NYC.

Thanks! Obviously one of my favorite artists too :)

Re: An illustrated introduction to linear algebra

#49

Post by Awesomedonut »

abirch wrote: post #39
ngriffiths wrote: post #32

I feel like it's obligatory to also drop a link to the 3blue1brown series on linear algebra, for anyone interested in learning - it is a step up from what's in this post, but these videos are brilliant and still super accessible: https://youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFit...

It’s crazy his framework is open source https://github.com/ManimCommunity/manim

One of my favourite internet things is seeing other channels, for instance Reducible (https://www.youtube.com/@Reducible) use the framework. Everyone has their own special take on it, and it's so awesome that Grant made it OS!
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