4 ms·

I don't find your function-composition slant motivating, though it is interesting. My linalg is self-taught, and I'd never seen / thought about the differences

I don't find your function-composition slant motivating, though it is interesting. My linalg is self-taught, and I'd never seen / thought about the differences between the row picture and column picture. These can be really useful when doing linalg by hand if you're e.g. trying to massage a system into a form that you can solve / code. It's useful to see that "oh, I don't have to multiply these out, I can just regroup them in this way because of the col or row picture." Here's my motivation for LinAlg: implementing physical simulation / graphics papers on the computer. Strang's sytle is a very good fit for that. I'm interested in a more abstract style for AI / knowledge rep issues, but it's not the first motivation. Er ... I should add that in Ontario / Canada we did matrix multiplication in high school, so the university "first course" wasn't really a first course. Not sure about now, though.

btilly 17y ago
There are two very different ways of approaching basic linear algebra. Given that you only understand one approach, how can you presume to judge the trade-off between the two methods? My firm belief from having learned and taught the subject is that the linear function approach is superior. For instance when you are discussing concrete algorithms for physical simulations, it makes it easy to connect your understanding of the physical process you are trying to model with the equations you write down. That is because you understand how the matrix of numbers represents what you are trying to do. By contrast having people write down long calculations and gain practice eventually leads to competency through familiarity, but in my opinion it takes longer before the math starts "connecting" to mental models of what is being written down.

4 ms·

I don't find your function-composition slant motivating, though it is interesting. My linalg is self-taught, and I'd never seen / thought about the differences

by JabavuAdams 17y ago

btilly 17y ago
There are two very different ways of approaching basic linear algebra. Given that you only understand one approach, how can you presume to judge the trade-off between the two methods? My firm belief from having learned and taught the subject is that the linear function approach is superior. For instance when you are discussing concrete algorithms for physical simulations, it makes it easy to connect your understanding of the physical process you are trying to model with the equations you write down. That is because you understand how the matrix of numbers represents what you are trying to do. By contrast having people write down long calculations and gain practice eventually leads to competency through familiarity, but in my opinion it takes longer before the math starts "connecting" to mental models of what is being written down.