Let's show that this definition is equivalent to the orthogonal group is the group of all matrices that preserve the dot product.

Note that:and for that to be true for all possible $x$ and $y$ then we must have:i.e. the matrix inverse is equal to the transpose.

Conversely, if:is true, then

These matricese are called the orthogonal matrices.

TODO is there any more intuitive way to think about this?

Framework built on top of React.

Officially recommended by React^[ref]:

gothinkster/realworld blog example by Ciro Santilli: node Express Sequelize Next.js realworld example app.

Basically what this does is to get server-side rendering just working by React, including hydration, which is a good thing.

Next.js sends the first pre-rendered HTML page along with the JavaScript code. Then, JavaScript page switches just load the API data.

Next.js does this nicely by forcing you to provide page data in a serialized JSON format, even when rendering server-side (e.g. the return value of getServerSideProps). This way, it is also able to provide either the full HTML, or just the JSON.

Some general downsides:

In theory, Next.js could be the "ultimate frontend framework". It does have a lot of development difficulties that need to be ironed out, but the general concepts, and things it tries to integrate, including e.g. webpack, TypeScript, etc. are good. Maybe the question is when will someone put it together with an amazing backend library and dominate and finally put an end to the infinite number of Js Frameworks!

In-tree examples at: github.com/vercel/next.js/tree/canary/examples

canary is their master: github.com/vercel/next.js/issues/3211

In order to offer its amazing features, Next.js is also extremely opinionated, which means that if something wasn't designed to be possible, it basically isn't.

No prerender with custom server? It forces you to write your API with next as well? Or does it mean something else?

TODO can it statically generate pages that are created at runtime? E.g. if I create a new blog post, will it automatically upload a static page? It seems that yes, and that this is exactly what Incremental Static Regeneration means:However, Ciro can't find any mention of how to specify where the pages are uploaded to... this is pat of the non-Vercel deployment problem.

Can't ISR prerenter by URL query parameters:That plus the requirement to have one page per file under pages/ leads to a lot of useless duplication, because then you are forced to place the URL parameters on the pathnames.

"Module not found: Can't resolve 'fs'" Hell. The main reason this happens seems to be the that in a higher order component, webpack can't determine if callbacks use the require or not to remove it from frontend code. Fully investigated and solved at:

Overviews:

TODO answer:

An IBM made/pushed term, but that matches Ciro Santilli's general view of how we should move forward AGI.

Ciro's motivation/push for this can be seen e.g. at: Ciro's 2D reinforcement learning games.

One of Satoshi's email addresses, it's how he made the First public announcement of Bitoin on first public announcement of Bitcoin on 2008-10-31.

At some point later on vistomail.com was discontinued and acquired by a super dodgy dude, Alex Elbanna, so it hasn't been Satoshi for a while.

List of instruction set architecture.