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EDIT: I'm leaving this here to help anyone else who might have been confused by this, which I imagine is likely. What confused me is that the author is not treating the matrix as a function from vectors to vectors, as is the customary way to treat matrices as functions. Rather, they're using the matrix to represent a sparse, regular sampling of a function from vectors to scalars. --- This article makes no sense right…
Earlier quoted context omitted.
Wow! It seems you have the magical capacity to ingest the reference to an equation and instantly derive an intuition for how it works and what it's useful for. Learning technology this advanced has never been seen before by humankind, I hope you share it with the rest of us!
Everything being referenced is stuff you'd learn in a typical technical education as part of either calculus or statistics. Your reply comes off as of defensive in a way that implies that you're shocked some one would know any of this stuff.
Sorry but can there be more context to why it is a powerful tool?
This is a typical issue with HN posts. Some poor soul wrote a somewhat competent and maybe even lengthy blog post / article about something they really care about and are knowledgeable about. It may be directed at a specific audience, or maybe just screaming into the void to record down some insight they had for themselves to read again later, or similar. And they use a more-than-necessary general title like "the bes…
The dilemma with titles is that most of them fall into one of two categories:
- titles where the author didn't put much effort into
- titles where the author tried too hard
The first category is often confusing because the article doesn't fit the title well. The second category often ends up as clickbait.
EDIT: I'm leaving this here to help anyone else who might have been confused by this, which I imagine is likely. What confused me is that the author is not treating the matrix as a function from vectors to vectors, as is the customary way to treat matrices as functions. Rather, they're using the matrix to represent a sparse, regular sampling of a function from vectors to scalars. --- This article makes no sense right…
EDIT: I'm leaving this here to help anyone else who might have been confused by this, which I imagine is likely. What confused me is that the author is not treating the matrix as a function from vectors to vectors, as is the customary way to treat matrices as functions. Rather, they're using the matrix to represent a sparse, regular sampling of a function from vectors to scalars. --- This article makes no sense right…
Given the arguments to the function, locate the cell in the matrix and use its value as the result of the function.
Sorry but can there be more context to why it is a powerful tool?
The other ways of solving the example of arbitrary heat sources and sinks on a plate range from hacky combinations of simpler methods, to tedious math, to complicated general methods. If you switch from heat to pressure distribution, you'd have the same types of options, but the specific methods would be different.
Earlier quoted context omitted.
Wow! It seems you have the magical capacity to ingest the reference to an equation and instantly derive an intuition for how it works and what it's useful for. Learning technology this advanced has never been seen before by humankind, I hope you share it with the rest of us!
Everything being referenced is stuff you'd learn in a typical technical education as part of either calculus or statistics. Your reply comes off as of defensive in a way that implies that you're shocked some one would know any of this stuff.
Maybe an analogy would better explain my perspective. I imagine that enriquto would greatly appreciate my latest article, reproduced in its entirety below:
# Learn how to write a JSON parser
> j = JSON.parse("[1,2]")
Fin.
Basically the note-taking gizmo is a graph. Nodes are given conceptual masses either through pagerank or betweenness centrality (i.e. either through how many random walks or how many shortest paths cross a node). Then we calculate a potential energy (gravity potential) if we by inverting the graph laplacian (a few methods are available). Special attention is given to nodes that "float the most.
E: forgot to link to it! https://github.com/asemic-horizon/sursis/
Sorry but can there be more context to why it is a powerful tool?
This is a typical issue with HN posts. Some poor soul wrote a somewhat competent and maybe even lengthy blog post / article about something they really care about and are knowledgeable about. It may be directed at a specific audience, or maybe just screaming into the void to record down some insight they had for themselves to read again later, or similar. And they use a more-than-necessary general title like "the bes…
I found it a throwback to my university years, but I did study Industrial Engineering with thermodynamics, fluid mechanics and whatnot so I did find it interesting. I'm pretty sure it's usable by a bunch of people in HN as well in many fields where software intends to emulate the real world, like designing a smart appliance, games, VR, etc.
Earlier quoted context omitted.
Also, what's confusing is that algebra usually uses matrices to describe linear functions from n-dimensional to m-dimensional vector spaces. Matrix has n rows, m columns, you give it an n-dim vector and after matrix multiplication you get back an m-dim vector. The author uses a matrix quite differently. You give it two integer coordinates i and j and it gives you the value at position (i, j) back. That's a valid use,…
Can you link to context for this? I learned both in linear algebra, so it seems like either would be just as 'expected'.
In linear algebra, we would interpret this as a linear map. A true equation would be f([1, 2, 3]^T) = [6, 6, 6]^T (where I'm using ^T to mean "transpose to a column vector").
But here, the author means f(1, 2) = 1, i.e. the (1,2) coordinate of the matrix is 1.