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Comment by zkmon | Hacker News Reader

I doubt anyone of the past or present could fully describe what a matrix is, and what its multiplication is. There are many ways people looked at it so far - as a spatial transformation, dot products and so on. I don't think the description is complete in any significant way.

That's because we don't fully understand what a number is and what a multiplication is. We defined -x and 1/x as inverses (additive and multiplicative), but what is -1/x ? Let's consider them as operations. Apply any one of them on any other of them, you get the third one. Thus they occupy peer status. But we hardly ever talked about -1/x.

The mathematical inquisition is in its infancy.

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As someone who never got deeply into math but deeply into programming they just seemed like an incompletely generalized data structure with an interesting "canonical" algorithm that can be used on it. In some cases, if you arrange your data into the structure correctly, you can use it to model interesting real world phenomenon.

It feels like Linear Algebra tries to get at the heart of this generality but the structure and operator is more constrained than it ultimately could be. It's a small oddball computational device that can be tersely written into papers and widely understood. I always find pseudocode easier to follow and reason about but that's my particular bias.

This is just low brow philosophical sounding rubbish of the same variety as "what is 'is'" nobody knows. Sounds profound though.

Matrix is just one way to organize data. When linear operators are organized this way composition of linear operators map to matrix multiplication.

But that is just one of the ways that multiplication may be defined on matrices, Hadamard products, Tensor product, Khatri-Rao product are some of the other examples. They all correspond to different mathematical structures one wants to explore or use. If linear algebraic structures is what ones to explore or use then one gets matrix multiplication.

I get your point, but i think the real issue is -(1/(-1/x)). It is the one that is being overlooked the most in our society, as if it were something normal, but it contains some of the deepest truths imho.

how about -1/(-(1/(-1/x))) ? How many roads must a man walk down before we can call him a man ?

No need of walking, they just need to be able to read post properly before calling him a man.

No you didn't get it. You missed "Let's consider them as operations. Apply any one of them on any other of them, you get the third one."

So is what i wrote a third one? Fourth? Fifth? :)

Not sure what you are talking about. What you wrote reduces to just x. What I meant was, if you substitute say, -x for x in -1/x, you get 1/x, which is the third inverse. Same is true for the other two pairs. So, if we call them functions f, g and h, then, f=g(h)=h(g); g=f(h)=h(f); h=f(g)=g(f)

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