OpenLLM-France/wikimedia huggingface dataset:
# Vector space/mxn-Matrices/Example

For a field $K$, and given natural numbers $m,n$, the set
    $\operatorname {Mat} _{m\times n}(K)$
of all $m\times n$-matrices with componentwise addition and componentwise scalar multiplication, is a $K$-vector space. The null element in this vector space is the null matrix
    $0={\begin{pmatrix}0&\ldots &0\\\vdots &\ddots &\vdots \\0&\ldots &0\end{pmatrix}}\,.$
# Linear system/n Variables/Solution space is (a 1,...,a n)/Exercise

Let $K$ be a field, and let
    ${\begin{pmatrix}a_{1}\\\vdots \\a_{n}\end{pmatrix}}\in K^{n}\,$
be a nonzero vector. Find a linear system of equations in $n$ variables with $n-1$ equations, whose solution space is exactly
    ${\left\{\lambda {\begin{pmatrix}a_{1}\\\vdots \\a_{n}\end{pmatrix}}\mid \lambda \in K\right\}}.$
# C++/Lessons/Data Structures

* Lesson 8: Pointers
* Lesson 9: Classes and Inheritance
* Lesson 10: Templates 1
* Lesson 11: Templates 2
# Learning the Basics of Landan/Learn the tenses

This page is designed as an introduction to the main tenses used in Landan. As of yet it is unfinished but we hope to cover, present, perfect, imperfect, future, near future, conditional, past historic and compound tenses.

### Present Tense

In Landan, verbs in the infinitive end in -en, or -n
| | EN | N |
| | Nehmen, to call, to name | Lehdn, to let |
| ig tu se sie nor ye sun Jau | nehme nehmst nehmt nehmt naamen naame nehmen naame | leht lest let let lessen lesse lehdn lesse |
Pronouns-
* ig - I
* tu - you
* se - he
* sie - she
* nor - we
* ye - you (plural or singular polite)
* sun - they
* Jau (formal you) - you

## Perfect Tense

The perfect tense is used to describe an action in the past that has been completed
The Past Tense is formed by the Auxiliary Verb and the Past Participle
Auxiliary Verb This is a 'helping' verb (eg. the have in 'I have danced') and in Landan we either use Eßn or Heben.
In case you don't know all of these verbs here they are in present tense, and below they're given in the perfect tense-
| | Heben (to have) | Eßn (to be) |
| ig tu se sie nor ye sun Jau | hebe hebst hebt hebt haben habe heben habe | ben bis is is essen esse eßn esse |
| | Heben (to have) | Eßn (to be) |
| ig tu se sie nor ye sun Jau | habte habst habt habt hatten hatte hatten hatte | war wes wis wis send sand send sand |

## The Perfect Infinitive

The perfect infinitive is formed with the infinitive of eßn or haben and the past participle.
The most frequent use of the perfect infinitive is with drutz.....heben or drutz.....eßn, meaning after having.
Drutz ett heben...
After having eaten...

# Past Participle

This is the part equivalent to the english verb part usually ending in -ed, (like jumped, in 'I have jumped')
This is formed differently depending on the verb ending-
* for all verbs, in the past participle, the declensions in the plural persons (except "they") are used in spelling. For instance, we saw that the verb "to watch, to witness"(kauschen) declined to "nor kuschen" (au=u). The same for "heben," the e becomes an a. In the past participle, regular verbs, and most irregular verbs adopt the prefix ge-, plus the participle endings.
Examples
kauschen - to watch yields gekuscht - watched sukern - to search yields gesugt - chosen flegen - to fly yields geflugt - flew
Irregular Past Participles
This is not all the irregular past participles in Landan.
eßn - bent - been lauchen - laft - laughed gahn - gant - gone konnen - gekomt - knew kannen - kann
# Learning the abc's

Teaching the abc's can be simple. Using books, flashcards and a good phonics curriculum can help. Make it fun! Kids love learning and will enjoy learning when all the senses are involved.
You can teach a letter a day and then look for things that start with that letter. For example, the letter A. Eat apples for lunch, cut out pictures of ants, anteaters, alligators, or airplanes.
But most of enjoy the learning process!
I agree that making it FUN is imperative for preschoolers. Yet with the pressures of kindergarten requirements rising, the preschooler is now having to learn by rote memorization, and testing as well.
This is not developmentally ready for such.
We, as educators, can make learning the ABC's exciting by hands-on learning. As suggested above cutting an apple talking about the letter A and the sound, yet they are exploring the texture taste and feel of that apple also therefore cementing the moment in their brain.
Creating teachable moments through play is highly suggested. The children do not even know that they are learning their three R's when presented with these type of learning environments. Yet the file this information for later use.
Samples of teachable moments: one; exploration tables wrapped around the letter you are wanting the child to learn. Have objects that start with that letter emphasize the sound when you are listening to the child/children exploring. Engage in their vocabulary have wipe off boards there as well to encourage their own writing. (remember that it may not be ledgeable (scribbles) Shaving cream to practice the shape of the letter. Hands on environments make learning fun and rewarding for the children and the teacher.
MKS of California

## Later

After your child has become proficient in the Alphabet would be apt to teach them some vocabulary
* The Alphabet
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
# Learning the Basics of French/Lesson:Introducing Yourself/2

Courses in French :
| Course #1: | Français I |
| Course #2: | Français II |
| Course #3: | Français III |
| Course #4: | Français IV |

## Vocabulary

Audio : French native speaker
Visiting Other Cities :
| 1a | Tu es d'où? (informal) | Where are you from? |
| 1b | D'où êtes-vous? (formal) | Where are you from? |
| 1c | Je suis de... (d') | I am from... |
French Vocabulary • 2 • audio: One • Two • (v2 300kb) (250 + 234 +186 kb • help) Nationalities Les nationalités :
| Masculine | Feminine | English |
| allemand | allemande | German |
| américain | américaine | American |
| anglais | anglaise | English |
| australien | australienne | Australian |
| belge | belge | Belgian |
| birman | birmane | Burmese |
| cambodgien | cambodgienne | Cambodian |
| canadien | canadienne | Canadian |
| chinois | chinoise | Chinese |
| coréen | coréenne | Korean |
| espagnol | espagnole | Spanish |
| français | française | French |
| indien | indienne | Indian |
| indonésien | indonésienne | Indonesian |
| italien | italienne | Italian |
| japonais | japonaise | Japanese |
| malaisien | malaisienne | Malaysian |
| mauricien | mauricienne | Mauritian |
| néerlandais | néerlandaise | Dutch |
| philippin | philippine | Filipino |
| portugais | portugaise | Portuguese |
| singapourien | singapourienne | Singaporean |
| suédois | suédoise | Swedish |
| suisse | suisse | Swiss |
| thaïlandais | thaïlandaise | Thai |
| vénézuélien | vénézuéliene | Venezuelan |
| vietnamien | vietnamienne | Vietnamese |

## Grammar

French has six different types of pronouns: the 1st, 2nd, and 3rd person singular and the 1st, 2nd, and 3rd person plural.
French Grammar • 2 • audio (info •61 kb • help) Subject Pronouns Les pronoms personnels :
| 1st person | singular | je | I |
| 1st person | plural | nous | we |
| 2nd person | singular | tu | you |
| 2nd person | plural | vous | you |
| 3rd person | singular | il, elle, on | he, she, one |
| 3rd person | plural | ils, elles | they (masculine) they (feminine) |
Être translates as to be in English. It is an irregular verb, and is not conjugated like any other verb.
French Verb • 2 • audio (info •103 kb • help) être to be :
| | Singular | Singular | Singular | Plural | Plural | Plural |
| first person | je suis | jeuh swee | I am | nous sommes | noo sum | we are |
| second person | tu es | too ay | you are | vous êtes | voozett | you are |
| third person | il est | eel ay | he is | ils sont | eelsohn | they are (masc. or mized) |
| third person | elle est | ell ay | she is | ils sont | eelsohn | they are (masc. or mized) |
| third person | on est | ohn ay | one is | elles sont | ellsohn | they are (fem.) |
Its important to learn all these conjugations.
# Learning the Basics of French/Lesson:Introducing Yourself/3

Courses in French :
| Course #1: | Français I |
| Course #2: | Français II |
| Course #3: | Français III |
| Course #4: | Français IV |
# Learning the Basics of French/Lesson:Introducing Yourself/1

Courses in French :
| Course #1: | Français I |
| Course #2: | Français II |
| Course #3: | Français III |
| Course #4: | Français IV |
Continuons!
# Learning the Basics of landan/Introducing Yourself

TEXT - SCHEEST
EX 1
Frank: Morgen! Wo gahnest tu?
Berte: Got, eind tu?
Frank: Fhenst!
EX 2
Frank: Gotdag sir! Wo gehe Jau ?
Berte: Fhenst! Eind Jau??
Frank: Fhenst!
EX 3
Frank : Berte, leht mie Kipp dig vorrbrengen .
Kipp : Enchanté.
Berte : Vorrlehrngot!
How do you introduce yourself?:
(-How do you use your free time?-)
How do you spend your vacation?:
(-What do you do on your vacation?-)
VOCABULARY - PRAGKTWERDS
In Landan, all nouns are either masculine or feminie.
GRAMMAR NOTES - GRAMMARNOTES
Verbes amt hierkuft - Verbs in the present tense
GAHN (TO GO):
      * ig gahne
      * tu gahnst
      * se gahnt
      * nor gehen
      * ye gehe
      * sun gahn
      * Jau gehe
VORRBRENGEN (TO INTRODUCE):
      * ig vorrbrenge
      * tu vorrbrengst
      * se vorrbrengt
      * nor vorrbratten
      * ye vorrbratte
      * sun vorrbrengen
      * Jau vorrbratte
JEUHEN (TO PLAY):
      * ig jeuhe
      * tu jeuhest
      * se jeut
      * nor jouen
      * ye joue
      * sun jeuhen
      * Jau joue
(to be completed)
# Linear system/3 Variables/Solution space is (3,2,-5)/Exercise

Let $K$ be a field. Find a linear system of equations in three variables, whose solution space is exactly
    ${\left\{\lambda {\begin{pmatrix}3\\2\\-5\end{pmatrix}}\mid \lambda \in K\right\}}.$
# Introduction to C programming/Lectures/Introduction
## What is debugging?

Debugging is searching for mistakes in your program. No one is perfect, we all make mistakes. Despite having programmed for nearly a decade, I made several errors while writing the first few programs for this class. If you're going to program, you're going to need to learn to debug. This class will teach some basic debugging techniques and common mistakes along with the rest of the material. Don't treat this as a minor part of the class - you will generally spend more time debugging a program than you will writing it.

## Software engineering

Software engineering is a set of habits and practices that help to make your code easier to read and understand. The easier your code is to understand, the fewer bugs it will have, and the easier they will be to find. It will also make it easier to maintain when you find a bug or want to add a new feature 6 months from now. Trust me, you won't remember how you wrote the code, no matter how much you think you will. Its always best to get into good habits early, so the class will try and teach you how you should do things, as well as just the syntax of the language. Remember, writing good code isn't just for yourself - it helps your coworkers and anyone else who ever has to work with your code.
# Walsh permutation; bit permutation

The term bit permutation was chosen by the author for Walsh permutations whose compression matrices are permutation matrices.
Ordered in rows like the corresponding finite permutations ( A055089) they form the infinite array  A195665.

## 3-bit

An extract of the table of 3-bit Walsh permutations:
| | CV | D | Σ | # | Permutation Inversion Vector | IN | Cy |
| 0 | 1 2 4 | + | 3 | 0 | 0 1 2 3 4 5 6 7 0 0 0 0 0 0 0 0 | 0 | &1  0 |
| 1 | 2 1 4 | − | 3 | 722 | 0 2 1 3 4 6 5 7 0 0 1 0 0 0 1 0 | 2 | &2  3 (2+2)> |
| 2 | 1 4 2 | − | 3 | 288 | 0 1 4 5 2 3 6 7 0 0 0 0 2 2 0 0 | 4 | &2  3 (2+2)> |
| 3 | 4 1 2 | + | 3 | 1032 | 0 2 4 6 1 3 5 7 0 0 0 0 3 2 1 0 | 6 | &4  9 (3+3)> |
| 4 | 2 4 1 | + | 3 | 2210 | 0 4 1 5 2 6 3 7 0 0 1 0 2 0 3 0 | 6 | &4  9 (3+3)> |
| 5 | 4 2 1 | − | 3 | 2354 | 0 4 2 6 1 5 3 7 0 0 1 0 3 1 3 0 | 8 | &2  3 (2+2)> |

## 4-bit

Applying a permutation p$_n$ of 0,...,3 on the reverse binary digits of numbers 0,...,15 gives a permutation P$_n$ of these 16 elements.
p$_{23}$ permutes (0,1,2,3) into (3,2,1,0). P$_{23}$ = wp(2$^3$,2$^2$,2$^1$,2$^0$) = wp(8,4,2,1) is the 4-bit bit-reversal permutation.
Applying all permutations p$_0$,...,p$_{23}$ of 0,...,3 on the digits of 0,...,15 gives the bit permutations P$_0$,...,P$_{23}$, which also form the symmetric group S$_4$. But the big permutations have to be composed in a different way, to get corresponding results: $p_{a}*p_{b}*...=p_{x}~~~~\Leftrightarrow ~~~~...*P_{b}*P_{a}=P_{x}$
See example calculations.
Walsh permutation; inversions#Bit permutations
# Introduction to C programming/Variables

variables are used to store values in a program. Just like in algebra. There are 3 types of variables in C-programming, character, integer, and float. A character is, well simply a character such as 'v' or 'a' or 'h'. An integer is a whole number, such as '5' or '10' or '19086'. A float is a decimal number, such as '4.26' or '3.14' or '5.679'.
Before you can store a value in a variable you have to declare it. By declaring a variable your telling the compiler to "take this variable, and make room for a value in the computers memory". then you can define it.
Lets say I wanted to make variable a to be an integer with a value of five. I would do this:
int a; a = 5;
the first line of code (int a;) declares a as an integer. Then a=5 makes the variable a have a value of 5. As you may have noticed, there is an int before a. This is use to declare an integer. To declare a character, you would use char before a and make sure the variable is being declared as a character. You would use float before a to make it a float.
# Introduction to C programming/What you need before you can learn

OSX:
FreeBSD: You can use clang directly by invoking "clang" or may use the default compiler using "cc". You may also install gcc by running "pkg install gcc" or by installing the devel/gcc port.
# Introduction to C programming/Hello World

If you have not installed the applications cited in the Software Needed section, please do so before moving on!

## Hello World

The first application that almost every programmer begins with is the "Hello World" application. This is a very simple application that only prints a line of text to the terminal window. This lesson will demonstrate the basic principles and techniques that are used when designing more in-depth applications.
The process is simple: open your text editor, (emacs, Xcode, etc...) and type in the following text:
Next, save your text file as "hello.c" or something similar. It is very important that the file has the extension ".c" instead of anything like ".doc" or ".txt".
--Mashedmeat 04:37, 11 March 2009 (UTC)
# C Programming/Data types
### What comes below the basic data types?

Each of the primitive data types learned here are one of two types: integral or floating point. Integral types store a literal integer in RAM - the sequence 1001 0011 1101 0111 in RAM represents exactly that number, in base-2, for the purpose of math performed upon it. Any int type (eg. int, long int, uint, int8_t, uint8_t etc.) or char type (eg. char, signed char, unsigned char) is an integral type. The reason a char works this way is because, when printed, the machine writes the values to memory containing the file (if you use a unix-like OS. The file is stored in RAM). Then when displaying this, the GPU displays in the correct position the pixels for each character in memory that is visible through the window. Note that a character can be by default either signed or unsigned - it doesn't technically matter, since it should only be used for characters, unless you want to use the int8_t/uint8_t,which are defined as signed char/unsigned char (if you use an 8-bit-char CPU). Note that these types can only store whole numbers - by which it is meant their memory, when used in any sort of math, as treated as representing a whole number, by which in turn it is meant that math the CPU does using only these types produces an output as if they were treated as being done with the numbers an base-2 integers. If you use an integral and a floating-point type, then the integral type is first converted into its representation as a floating-point number. The floating-point type in C is represented by all float and double types. The same keywords are available for integral and floating-point types, excluding the signedness factor, due to the way the number is stored in memory. Generally, a float is stored, for an n-bit number, as follows: 1st bit: represents the signedness, can be viewed as a plus-or-minus. This method of representation is why all floating-point types MUST be signed. 2nd to xth bits: represents the exponent. The radix to which the exponent is taken is system-defined. xth to nth bits: represents the significand. All floating-point math (should) take in only floating-point types, and output a floating point type. All floating-point math is done in a special unit of the CPU, called the FPU.

### void type

void type has 0 size and cannot be used as a type. The only time it's used is when doing pointer-type conversions. Note that, confusingly, when a void-pointer is accessed (ie. the value which should be void), a single byte is accessed (if possible). The main reason for not causing an error is probably that a void pointer is used for functions to move data, and constant conversions being written in the code, while not slowing it down, can obfuscate it, plus the void-pointer already stores an actual memory address to access.
# Introduction to Programming C/Lectures/Variables
## Naming again

Since naming is by far the most important thing to take away from this lesson, I'm going to hit it again. Choosing good names is one of the most important thing to do when writing code. It will do more for making your code easy to read and understand than almost anything else. Its important to get in good habits now, too many programmers learn how to code and use x and y for all their variables. Lets use an example. Which of these give you the most information:
* int x;
* int myHeight;
* inches x;
* inches myHeight;
The first tells you nothing. The second tells you whats being stored, but not how its represented (inches? centimeters? microns?). The third tells you how something is being stored, but not what it is. The final one tells us not only what's being stored, but how its represented. Now imagine a large program with 10,000 variables. Which do you think will take you less time to understand? So be kind to your fellow programmers, and use descriptive names.
# Learning on Twitter

Twitter can be used for learning. This is about how to best utilize Twitter for research, learning, and teaching.
What do you want to learn about on Twitter?
Reddit can also be utilized for learning, teaching, and research.

## Discussion questions

* How might you use Twitter for learning?
* How might you utilize Twitter for research?
* What do you want to learn about on Twitter?
* What can you teach others on Twitter?

## Educational Twitter feeds

* Short educational video clips from NASA
* Pew Research Center on Twitter
* Official NASA Twitter feed
* International Space Station Research on Twitter
* BBC Learning on Twitter
* Khan Academy
* Sustainability at Portland State University
* Smithsonian Learning Lab
* Education Week
* Federal Educational Resources
# Introduction to C programming/Lectures/BooleanLogic
## Variables and comparisons

You don't have to compare only numbers. You can also compare either a variable and a number (for example- x<7), or two variables (for example, x>y). When you compare a variable to something, what you really do is compare the value of the variable to either a number or another variable's value.

## If statements

Well thats fun, but how does C allow you to make a decision? You use an if statement. An if statement allows a program to run a series of lines if and only if a condition is true. An if statement looks like this:
where condition is a boolean expression of some sort.
Anything inside the block will only happen if condition is true. If its false, they aren't executed. You can have as many statements in the block as you want.

### Else clauses

Sometimes you don't want to just do soemthing if a condition is true. Sometimes you want to do one thing if its true, and another if its false. An else statement looks like this:
Anything inside the first happens if the condition is true, and the code inside the second block happens if it is false.

### Else if statements

Occasionally, you need something a little more complex than 2 options. In that case, you need an else if.
If condition 1 is true, statement 1 is executed and none of the other statements are. If condition 1 is false and condition 2 is true, statement 2 is run. If conditions 1 and 2 are both false and condition 3 is true, statement 3 is run. If all 3 conditions are false, statement 4 is run. You can have as many else if parts as you want. And you don't need to have an else at the very end if you don't want to.

### Switch statements

Switch statements are a quick way of writing large else if statements where you're checking the value of a single variable. For example, if you want to do different things depending if a variable is 1, 2, 3, 4, or 5, a switch statement can be used. A switch statement works like this:
If the value of variable is value1, statement 1 is executed. If its value 2, statement 2 is. And so on.
Notice the word break; at the end of each case. This is actually important- if you don't put it in, you'll execute the next case as well. This can actually be useful- if you want to do the same thing for 2 values, you can go:
Here, if the variable is value1 or value 2, you'll execute statment 1. Be careful of your breaks, leaving one out by mistake is an easy bug to make. Even experienced pros make this one every once in a while.

## Boolean type

There's actually a boolean type in C. You can declare a variable of type bool, who's only legal values are TRUE and FALSE. You can use this to store true/false info in a program.

### The value of true and false

So, since everything in computers is a number, what values do true and false have? False is always 0, true is anything else. You can actually use an integer as a condition in an if statement. If the value is not zero, the if would be true, if its 0 the if is false. You'll see a lot of code, especially older code, using this feature.
# Learning resources

* Learning resources (Education) - links to learning resources for education
* Learning resource - Wikiversity learning project about Learning Resources
* Wikiversity:Learning resources - a guide to creating learning resources on Wikiversity

## Categorising Resources

* Category:Resources
* Category:Resources by completion status‎
* Category:Resources by level
* Category:Resources by need‎
* Category:Resources by project‎
* Category:Resources by type‎
* Category:Resources by who participants are
* Category:Resource centers‎
* Category:Resources under construction‎
* Category:Resources with an attribution‎
* Category:Resources with disclosures‎
* Category:Resources with related material‎
* Category:Featured resources‎
* Category:Completed resources
* Category:Nearly complete resources‎
* Category:Half-finished resources
* Category:Partly developed resources
* Category:Freshly started resources

## See Also

* Portal:Learning Projects - a guide to existing Wikiversity learning projects
* Portal:Learning Materials - a guide to existing Wikiversity learning materials
* Resources_favored_by_women
* Wikiversity:Being educational
* Wikiversity:Learning materials - general information about Wikiversity learning materials
* Wikiversity:Learning projects - general information about Wikiversity learning projects
# Linear mapping/Eigenspace for different eigenvalues/Zero/Fact/Proof

Let $v\in \operatorname {Eig} _{\lambda _{1}}{\left(\varphi \right)}\cap \operatorname {Eig} _{\lambda _{2}}{\left(\varphi \right)}$. Then
    $\lambda _{1}v=\varphi (v)=\lambda _{2}v\,.$
Therefore,
    $(\lambda _{1}-\lambda _{2})v=0\,,$
and this implies, because of $\lambda _{1}\neq \lambda _{2}$, $v=0$.