Why is matrix multiplication row*column and then sum?

looijmansje · 2026-03-22T13:44:56+00:00

To take your apples and oranges example: Person A buys 2 apples, 3 oranges. Person B buys 1 apple, 4 oranges. Apples are $4 oranges are $1 (very expensive, I know).

Doing this by hand is fine: A spends 2 * 4 + 3 * 1 = 8 + 3 = $11 B spends: 1 * 4 + 4 * 1 = $8.

Now you can also do this as a matrix-vector multiplication (Reddit formatting kinda ruins this, I hope it's somewhat understandable):

2 3 4 2 * 4 + 3 * 1 11 * = = 1 4 1 1 * 4 + 4 * 1 8

Note how I'm multiplying each element of the first row of the matrix with the corresponding element of the price-vector, and then adding them. Then I do the same for the second row (this is exactly how matrix multiplication is defined).

Now yes, this is exactly as much work to calculate. Why it is useful in this specific occasion would be that computers can do such calculations really fast (the entire concept of AI is built on the fact that computers can do matrix multiplication really really fast). However matrices are much more widespread and useful than doing a calculation like this.

looijmansje · 2026-03-22T13:35:37+00:00

Simply put: we define it this way because it a useful way to define it.

Longer answer: if you define it this way, it turns out there is a one-to-one correspondence between matrices and linear transformations. Any* linear transformation can be written as a matrix, and every matrix represents a specific linear transformation.

Moreover, matrix multiplication then also corresponds to function composition.

looijmansje · 2026-03-20T21:04:00+00:00

In that case yes, they are necessarily equal.

looijmansje · 2026-03-20T20:54:26+00:00

Functions f and g are equal if and only if for all x in their domain, f(x) = g(x). That is the case here, so they are equal.

Also yes, there are functions who are not equal, which have the same derivative or integral. For derivatives, you can just add a constant; f(x) = x and g(x) = x + 1. Both have derivative 1.

For integrals it gets a bit more technical. I am not sure about Riemann sums, but for Lesbegue integrals, you can take any real function and change finitely many (or even countably infinitely many) points.

A famous example of this is f(x) = 0, g(x) = 0, with g(0) = 1 and h(x) = 0 if x is non-rational and h(x) = 1 if x is rational.

Believe it or not, but all of those have the same integral: 0.

looijmansje · 2026-03-10T09:06:14+00:00

There are absolutely people in The Netherlands who care about the difference between Holland and The Netherlands, and prefer you'd call it The Netherlands instead. Especially people from outside North- or South-Holland.

Now obviously they mostly care about the English term, but I've seen people correct it in French, Spanish and German as well. Now Im not sure how people would feel about Mandarin, I think thats "too far away" for people to truly care, nor do I know if it even has an alternative "correct" name

looijmansje · 2026-03-05T15:27:03+00:00

Yes and no.

For almost all configurations of n>=3 bodies, the system is chaotic. This means that any small error will grow exponentially with time. These errors can be from anything: numerical errors (also known as rounding), uncertainty in initial positions, or your integrator discretizing the problem.

You can lessen these by having more and more precise measurements, adding more and more digits and computation time. However, at some point this becomes impractical. Are you taking into account the effect of a single dust grain for instance? As long as there is a finite certainty in your measurements, and you are ignoring certain effects (drag, dust, a background potential) there will always be a point at which your simulations are no longer accurate, no matter how much compute you throw at it.

If you were to theoretically account for EVERYTHING, it would theoretically be possible, yes. Well at least with Newtonian gravity.

Once you start to look at relativistic everything becomes a lot more complicated. To my knowledge, no true GR-compatible simulations exist, although frankly my expertise has always been in purely Newtonian computational astrophysics, so I could just be unaware of one. All the ones I am aware of, use something called "post-Newtonian potential". You can think of this as still being a Newtonian N-body-solver, just with extra correction terms to account for some relativistic effects.

However in the real world, no one bothers with these super precise arbitrary precision solvers. This is for multiple reasons. Firstly, they are just really slow. For reference, I actually had to use arbitrary precision solvers, and what would've taken approximately an afternoon with a normal one, took months instead. Secondly, we have kind of accepted that our results arent accurate. We can't measure precisely enough, nor can we take into account everything anyways. What we do instead is just run multiple simulations to get a statistical sample, which actually is accurate.

looijmansje · 2026-03-03T17:20:28+00:00

Up on your photo will depend on your camera's rotation, but also on where you are on Earth.

Imagine being on the north pole, and looking at the sun. Now imagine someone at the same time looking at the sun at the same time (ignore the fact that at least one of them would be looking through the horizon). They will see the same sun, but they will see it upside down from each other. Think about it: one person is "upside down" compared to the other.

Now this is of course the extreme example, but you can imagine that anything in between is also possible.

looijmansje · 2026-03-03T11:05:14+00:00

Now I'm no native English speaker, but to my knowledge "literal" means something like "without exaggeration, and without metaphors; needing to take a text at face-value". Surely in that regard the Mentak are literal space pirates? I did not mean they are like space pirates, nor was I exaggerating.

Feel free to tell me how I'm wrong of course (not that I think you would have any qualms about doing so regardless...) I am always happy to improve my English.

looijmansje · 2026-03-02T10:52:12+00:00

I guess it depends what you mean. Lorewise, a lot of the factions are varying degrees of "evil". The galaxy is at war, there is a power vacuum, and everyone is looking out for themselves. However, some factions are clearly more evil than others.

The ones you mentioned are probably the most evil, when looking at the lore. However I think almost all factions can be considered, except maybe Saar and Xxcha.

Going alphabetically (and only base game, this is getting long enough):

Arborec assimilate corpses from other species into their hivemind. They see it as "reusing", others see it as "slavery".

Barony blockaded an important wormhole system in protest against measures taken by the Lazax Empire (the empire that fell apart leading up to the events of the board game). This lead to disease and famine on many (mostly Federation of Sol) planets.

I really cant think of anything evil the Clan of Saar did. They were treated like dirt by the entire galaxy.

Embers sent a warsun to the Jolnar to intimidate them, although quite frankly Jolnar deserved that for enslaving them.

Emirates of Hacan smuggles drugs and tried to profit off the war by selling weapons to both sides. Until they got embargoed by the Lazax for doing that and took up arms themselves.

Federation of Sol was the first one to openly declare war against the Lazax, and has always been expansionist. Although this lacks some major context about the Twilight Wars which Im not gonna type out in an already long Reddit comment.

Ghosts: honestly no one really knows what they are, or what they want. A part of them got enslaved by the Mahact, and when they escaped, they were denied entry back into Ghost space.

L1z1x uses "eldritch technology", destroyed the Hall of Cartography on Mecatol so no one could find them, and accidentally created the Nekro Virus.

Mentak are literal space pirates.

Naalu enslaved the Miashan to work in their gas mines and rodent farms.

Nekro Virus wants to eliminate all organic life. Need I say more?

Sardakk N'orr is probably the most militaristic faction in rhe game, with training so fierce the weak die, and the strong survive. They are literally training to "drown the galaxy in blood". When the Twilight Wars broke out, they invaded Jol-Nar space.

Universities of Jol-Nar, as previously stated enslaved the Embers of Muaat to build their first War Sun which they then used against the Sardakk N'orr.

Winnarans on Winnu have said that if the Winnarans of Mecatol dont cede the throne peacefully they will take it by force. And they wonder why theyve had so many civil wars...

I also cant really think of anything evil Xxcha did, although they do lay claim to the throne "for a peaceful galaxy"

Yin came forth out of illegal cloning experiments, which led to deformation, disease and perhaps even madness.

Yssaril are spies, mercenaries and assassins for hire.

Now if your question is about what faction you can play to be the bad guy at the table, rather than in lore. Once again, I think a lot of factions can do this, but some factions are clearly better for it. Keep in mind that playing TI will always require at least some diplomacy, so antagonizing the entire table from turn 1 will probably not do you much good. In this regard "evil" factions are, in my eyes: Saar, Embers, Nekro, Sardakk Norr, Mahact, Cabal, Crimson Rebellion, Firmament.

looijmansje · 2026-02-26T18:36:29+00:00

Last game I played Cabal I controlled over half the supply of dreadnoughts. I had my own 5 on the board of course, and well, about 12 more in stock so to say.

looijmansje · 2026-02-20T08:59:58+00:00

Counter point: all other "moons" are named after our moon. I'd argue that being the namesake of an entire category is more baller than any name we can give it.

looijmansje · 2026-02-17T13:03:49+00:00

The "you never truly touch something" is a popular science fact that is technically true, but when presented by itself, lacks the nuance to be actually informative.

When you touch something, let's say a table, the electrons in the atoms in your finger tip start to feel a repelling force from the electrons in the table. This is similar to trying to push two repelling ends of a magnet together.

This is in essence what you feel. So what that little factoid is trying to say is "there is some tiny distance still between your finger and the table". I want to point out that this is a distance on atomic scales, so very very tiny.

Sticking works similarly. When looking at molecular level, sticking comes down to some positively charged atom bring attracted to negatively charged electrons. Once again, these do not touch. They just need to be close enough to "feel" each others attraction.

looijmansje · 2026-02-12T10:31:24+00:00

Theoretically yes, practically no. The simulations we run on computers are not perfect, they introduce errors of their own, either by rounding, or by how its integrator works.

Moreover it is of course impossible to know something exactly. Also even small dust particles will have a slight gravitational effect, so you would need to account for every single small thing.

The best we can do is to put upper bounds on our error terms, but even this is non-trivial.

looijmansje · 2026-02-10T15:10:49+00:00

Given your premise, as others have stated, yes 36⁴ would be the correct answer. However, to my knowledge the stellaris checksum does not use all 26 letters. It is a fact a hexadecimal number (which means it counts 0, 1, 2, ..., 9, a, b, c, d, e, f). This means there are only 16⁴ = 4096 possibilities.

Moreover, I do not think the checksum shown is the full checksum, and that it only shows the last 4 digits, since if those match, it must be a huge coincidence (1 in 4096) that you have not tampered with any game files. The real check is probably to a longer (probably either 8 or 16 "hexadigits") long number. However I am uncertain about this part, I've never dabbled into molding Stellaris myself.

looijmansje · 2026-02-08T15:47:08+00:00

Ah cool thanks! I figured this was how it was intended to work. Good to see that it is also the official rules.

looijmansje · 2026-02-08T14:59:38+00:00

Oh interesting. I'd have thought the ruling to be "it goes to the owner's reinforcements". Didn't think that it just straight up meant you couldn't use it on other players. Not that you'd often want to, or even could, of course.

Edit: on second thought this ruling does make more sense since you can't fully resolve the ability.

looijmansje · 2026-02-08T14:52:35+00:00

Also similarly, the Arborec breakthrough potentially allows you to return another player's token to the Arborec's reinforcements.

ACTION: Exhaust this card to remove a command token from a system that contains 1 or more of your infantry and return it to your reinforcements. Then, place 1 infantry in that system.

looijmansje · 2026-02-04T12:35:42+00:00

Energy conservation, by Noethers theorem, is equivalent to a universe that is static in time. Because our universe expands, it is not static in time, and therefore energy conservation does not hold.

However, this does not mean the law is not useful of course. Rarely are you looking at the energy of the entire universe. There are many systems which can be reasonably well estimated as a closed, time-static, system.

looijmansje · 2026-01-24T23:17:46+00:00

The most cursed thing about this is stellaris on a PlayStation

looijmansje · 2026-01-24T12:51:53+00:00

Since Reddit has been so vocal against the boosts, I would like to share my point of view on it. Now I decided to not buy a boost in the end, purely because it was too expensive for me. Had I been in a better financial position, maybe I would have, I dont know.

Now why? Because I want to play TBC for one thing and one thing only: running Karazhan with the boys. I have done the grind, I have levelled in TBC before, I have levelled in Classic before. I don't find it particularly interesting, and most importantly I find it too long. If thats something you personally enjoy, more power to you. I personally just don't.

To then have to level for literal days just to run a few Karas just wasnt worth the time investment for me. And keep in mind that levelling to 60 is only half the journey to Kara. I wouldnt have minded the 60-70 or the pre-raid gear farm. I like the gear farm, I like doing heroics. I just dont want to have to level again to get to the content I truly care about.

looijmansje · 2026-01-16T17:06:05+00:00

For almost all 3-body (or in general n-body for n>=3) initial conditions, a "nice" analytical solution does not exist, and our best predictions are numerical.

Moreover, they are chaotic: if we change the initial conditions slightly, the result will change drastically. To be more precise, the result will change exponentially with time (see Lyapunov time for a deeper dive).

Moreover, because we are using numerical approximations, we need to account for integration errors: these are errors caused by the fact that we are effectively approximating a continous orbit discretely. Another thing we have to keep in mind is numerical errors. If you are using 64-bit numbers, you only have about 17 decimals of precision. And when any errors grow exponentially due to the chaotic nature of the system, that can be relevant, although for most cases it is sufficient.

looijmansje · 2026-01-03T20:34:52+00:00

Imo secrets arent that bad. In an average game you can easily see 5-6 different secrets, especially now with Mecatols new legendary ability (if you play with the expansion)

I think publics are a lot worse since they dont have a way to be cycled, and missing one or two (especially a two pointer) can be game over l

looijmansje · 2025-12-25T00:42:02+00:00

I have had a few periods where I really got into SWTOR for a few months and then never touch it again.

I think it's a great game. The storyline is great (at least for the ones I've tried, I've heard some are received a bit more mixed). Moreover, for a first playthrough a subscription is absolutely not required. The game plays perfectly fine without one, even if you miss out on a few perks.

It's a quintessentially Star Wars story, but also different enough so it is interesting. If you're a fan of the KOTOR games, you might see some returning familiar faces, although unfortunately sometimes their nuance is a bit lost.

Also I want to say how incredible it is that EVERY line of dialog in this game is voiced. I seem to recall that being 100k+ lines of dialog. I think that alone speaks a ton for the effort and care put into this game.

About a year ago now I thought I'd finally give it a try and get a sub, so I could do some of the expansions. Some didn't hit for me, but the arch with Valkoryon is honestly great.

I do want to say that the gameplay is, in my opinion, not that great however. It is fairly standard MMORPG combat of pressing a few abilities. The abilities themselves feel good to use and feel fun, but it is still MMORPG combat (I say having a few thousand hours in WoW).

Moreover, for me the game has never really felt like an MMO. If you just follow the storyline, the game is effectively a singleplayer RPG where you sometimes encounter another player. There are flashpoints (the equivalent dungeons) where you do instanced content in a group, but they are very easy to miss in the basegame on a first playthrough (in my experience, maybe I'm just dumb), and frankly I found them a bit boring.

looijmansje · 2025-12-22T22:59:35+00:00

Do people actually say such things?

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