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How they are assigned: www.quora.com/How-are-MAC-addresses-assigned Basically IEEE gives out the 3 first bytes to device manufacturers that register, this is called the organizationally unique identifier, and then each manufacturer keeps their own devices unique.

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Organizationally unique identifier by

Ciro Santilli 37 Updated 2025-07-16

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Internet Protocol by

Ciro Santilli 37 Updated 2025-07-16

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IP address by

Ciro Santilli 37 Updated 2025-07-16

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Video 1.

The Internet Protocol by Ben Eater (2014)

Source.

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Dot product by

Ciro Santilli 37 Updated 2025-07-16

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The definition of the "dot product" of a general space varies quite a lot with different contexts.

Most definitions tend to be bilinear forms.

We use the unqualified generally refers to the dot product of Real coordinate spaces, which is a positive definite symmetric bilinear form. Other important examples include:

the complex dot product, which is not strictly symmetric nor linear, but it is positive definite
Minkowski inner product, sometimes called" "Minkowski dot product is not positive definite

The rest of this section is about the

R^{n}

case.

The positive definite part of the definition likely comes in because we are so familiar with metric spaces, which requires a positive norm in the norm induced by an inner product.

The default Euclidean space definition, we use the matrix representation of a symmetric bilinear form as the identity matrix, e.g. in

R^{3}

M = 100010001

(1)

so that:

x \cdot y = [x_{1} x_{2} x_{3}] 100010001 y_{1} y_{2} y_{3} = x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3}

(2)

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Positive definite symmetric bilinear form by

Ciro Santilli 37 Updated 2025-07-16

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Symmetric bilinear form that is also positive definite, i.e.:

\forall x, B (x, x) > 0

(1)

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Quadratic form by

Ciro Santilli 37 Updated 2025-07-16

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Multivariate polynomial where each term has degree 2, e.g.:

f (x, y) = 2 y^{2} + 10 y x + x^{2}

(1)

is a quadratic form because each term has degree 2:

$y^{2}$
$x y$
$x^{2}$

but e.g.:

f (x, y) = 2 y^{2} + 10 y x + x^{3}

(2)

is not because the term

x^{3}

has degree 3.

More generally for any number of variables it can be written as:

f (x_{1}, x_{2}, \dots, x_{n}) = \sum_{i, j} a_{i} a_{j} x_{i} x_{j}

(3)

There is a 1-to-1 relationship between quadratic forms and symmetric bilinear forms. In matrix representation, this can be written as:

x^{T} B x

(4)

where

x

contains each of the variabes of the form, e.g. for 2 variables:

x = [x, y]

(5)

Strictly speaking, the associated bilinear form would not need to be a symmetric bilinear form, at least for the real numbers or complex numbers which are commutative. E.g.:

[x y] [0210] [x y] = [x y] [y 2 x] = x y + 2 y x = 3 x y

(6)

But that same matrix could also be written in symmetric form as:

[0 1.5 1.5 0]

(7)

so why not I guess, its simpler/more restricted.

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 Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.

Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!

Video 1.

Intro to OurBigBook

. Source.

We have two killer features:

topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
Articles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1.
Screenshot of the "Derivative" topic page
. View it live at: ourbigbook.com/go/topic/derivative
Video 2.
OurBigBook Web topics demo
. Source.
local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
Figure 2.
You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
.
Figure 3.
Visual Studio Code extension installation
.
Figure 4.
Visual Studio Code extension tree navigation
.
Figure 5.
Web editor
. You can also edit articles on the Web editor without installing anything locally.
Video 3.
Edit locally and publish demo
. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
Video 4.
OurBigBook Visual Studio Code extension editing and navigation demo
. Source.
Internal cross file references done right:
Infinitely deep tables of contents:
Figure 6.
Dynamic article tree with infinitely deep table of contents
.
Live URL: ourbigbook.com/cirosantilli/chordate
Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade

All our software is open source and hosted at: github.com/ourbigbook/ourbigbook

Further documentation can be found at: docs.ourbigbook.com

Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact

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 Pinned article: Introduction to the OurBigBook Project