OpenLLM-France/wikimedia huggingface dataset:
# S. W. R. D. Bandaranaike

Solomon West Ridgeway Dias Bandaranaike (සොලමන් වෙස්ට් රිජ්වේ ඩයස් බණ්ඩාරනායක - சாலமன் வெஸ்ட் ரிட்ஜ்வே டயஸ் பண்டாரநாயக்கா; 8 January 1899 – 26 September 1959) is the fourth Prime Minister of Sri Lanka, serving his term from 1956 until 1959. He was shot while he was the Prime Minister of Sri Lanka by Talduwe Somarama, a Buddhist Monk.

## Early life

Bandaranaike was born on 8 January 1899 in Colombo, Ceylon to a Christian family, and had Solomon Dias Bandaranaike, the Maha Mudaliyar (the chief native and advisor to the Governor) of Horagolla Walauwa in Atthanagalla, as a father. In order to join Sri Lankan Politics, he converted into Buddhism. later in life. He received his secondary education at St Thomas' College and went on to study modern greats at Christ Church, Oxford University, where he was Secretary of the famous Oxford Union.

## Political Career

As said before, Bandaranaike converted into Buddhism in order to join politics. Bandaranaike was very active in the Ceylon National Congress (CNC). He was elected in 1926 to the Colombo Municipal Council (CMC). He then served in the State Council of Ceylon from 1931 to 1947. Bandaranaike wanted to raise Sinhalese culture, so he created the Sinhala Maha Sabha (SMS) in 1936. In 1946, he backed away from the United National Party (UNP). He then established the Sri Lanka Freedom Party (SLFP) in 1951.
Bandaranaike then became the fourth Prime Minister of Sri Lanka in the 1956 elections in a landslide, at the head of a four-party coalition with a no-contest pact with the Lanka Sama Samaja Party and the Communist Party of Sri Lanka. As SWRD wanted, he made Sinhalese the official language of the country, affecting the Sri Lankan Politics for over decades (which erupted the Tamil Tigers, the terrorist group).
As said by most, Bandaranaike made Sri Lanka into the country now is. And he caused a lot of problems, such as removing British air bases in Katunayake and China Bay and removing the naval base at Trincomalee. And Bandaranaike's failure into forgetting about the Sri Lankan Tamils let to many casualties of Tamils in the 1950 riots.

## Assassination

SWRD Bandaranaike was shot by a disgruntled monk named Talduwe Somarama on September 25, 1959, and died the day after.

## Sources

* http://www.britannica.com/EBchecked/topic/51488/SWRD-Bandaranaike
* http://dbsjeyaraj.com/dbsj/archives/1101
# History of Sri Lanka/John Kotelawala

Sir John Lionel Kotelawala, KBE, CH, KStJ, CLI (Sinhalese: ශ්‍රිමත් ජොන් ලයනල් කොතලාවල; 4 April 1897 – 2 October 1980) was a Sri Lankan soldier and politician. He was the third Prime Minister of Ceylon from 1953 to 1956.

## Early life and family

Sir John Kotelawala was from a rich family. His father, John Kotelawala Senior, was an inspector in the Ceylon Police Force. His mother was Alice Attygalle. John Kotelawala Snr committed suicide when his son was 11. The family were in ruins, Alice Attygalle converted to Christianity from Buddhism. He attended the same Royal College, Colombo, but dropped out after independence riots in 1915.
Thereafter he took a trip to Europe after leaving school, which was very dangerous because World War I was being fought there, he stayed in Europe for five years, spending most of that time in England and France and attending Christ's College, Cambridge, University of Cambridge to study farming.
Kotelawala was known as a strict man who loved sports, horseback riding, cricket and particularly as a young man, got into fights when he was made fun of. He knew Sinhala, English and French. After returning to Ceylon, he took up managing his family's "farm" and mines.

## Military career

He went on to serve 23 years mostly as a reservist (meaning a back up) since the Ceylon Defense Force was a army reservist of the British Army. In 1939 he became the commanding officer of the Ceylon Light Infantry and was promoted to the rank of Lieutenant Colonel in 1940. With the start of World War II, he became a member of the Ceylon's War Cabinet and was made a Colonel in 1942, the highest rank that a Ceylonese could achieve. Making himself a respectful man.
A strong supporter of the military, he was the first Chairman of the Ceylon Light Infantry Association in 1974. He was promoted to the rank of general on his deathbed.
He gave his home to the government to establish a national defense academy.

## Political career

As early as 1915, Kotelawala had become interested in political leaders such as Don Senanayake and his brother F.R. Senanayake, who was married to Kotelawala's mother's sister.
He entered politics by being elected to the Legislative Council as the member of Kurunegala. Thereafter he entered the State Council as a backbencher and was re-elected in 1936. In his second term he was appointed Minister of Communications.
# Global Audiology/Asia/Republic of Korea

| Home | Africa | Americas | Asia | Europe | Oceania |
| China | Hong Kong | India | Iran | Iraq | Japan | Korea | Nepal | Pakistan | Philippines | Saudi Arabia | Singapore | Thailand | Turkey | Vietnam |

# Brief Country Information

Located at the center of Northeast Asia, the Korean Peninsula neighbors China, Russia, and Japan. Under the World Geodetic System, it lies between 33 and 43 degrees north latitude and 124 and 132 degrees east longitude. The Peninsula (including both North and South Koreas) is 1,000 km long and 300 km wide on average, and its total land area is 222,000 km$^2$. The total land area of South Korea (below the Military Demarcation Line) is around 100,364 km$^2$.
Around 3/4 of the area is covered with mountains. You can find mountains almost anywhere in the country, but there are a few places you can view flat horizons. Topologically, Korea is higher in the east and lower in the west. Tall mountains with altitudes exceeding 1,000 m are concentrated in the north and the east, forming the topological backbone of the country. The mountainsides are steeper toward the east coast, and less severe toward the west coast.
Korea is surrounded by the sea on three sides, except for the northern side. The total extension of the coastlines is 17,000 km (including islands). The East Sea is characterized by its deep waters and simpler coastlines, whereas the West and South Seas are shallower, with complicated coastlines and more islands. Each of the three seas offers distinctive features and a wide array of oceanic atmospheres: the East Sea with its clean and deep water; the West Sea with its mud flats thriving with life; and the South Sea with its numerous islands (which earned the sea its nickname: Dadohae, or the sea of many islands).
South Korea has the 29th largest population in the world at around 51.63 million as of 2022. However, 50.49% of the population lives in the Seoul Capital Area (SCA, mainly consisting of Seoul and Gyeonggi-do), indicating severe population gaps among regions.$^1$

# Information About Audiology
### Audiological Societies and Medical Advancements in Korea

The Korean Audiological Society
Korean Academy of Audiology
37th World Congress of Aduiology

# References

* Ministry of Culture, Sports and Tourism https://www.korea.net/AboutKorea/Society/South-Korea-Summary
| | Contributor to the original text |
| Junhui Jeong | Contributor to the original text |
# Aristotle

While both are dear, piety requires us to honor truth above our friends. -- Aristotle, defending his rejection of Plato's Theory of the forms

## Classic and Scholastic Expositors

* Isagoge (Introduction) to Aristotle's Categories by Porphyry
* Guide to the Perplexed, by Maimonides

## Course

DEPRECATED - see associated wikipedia articles for information, and consider contributing to Aristotle for Everybody
* Life and Works
* Phenomenology of Knowledge - Categories, Topics, Sophistic refutations
* Logic and Linguistics - Prior Analytics, Hermeneutics
* Natural philosophy and science - Physics, Posterior Analytics
* Biology and Psychology
* Ontology and Metaphysics
* Cosmology and Theology
* Ethics and Politics
* Legacy

## Related resources

* Natural Science 14-17th century. A paper that covers Aristotelianism in the 14th to the 17th century CE.
* Doctrine of Change. Excerpts from Aristotle's Physics.
* On the Soul: Outline. Outline of Aristotle, On the Soul.
* On the Soul: discussion group. Discussion group.
* Aristotle's Categories and Topics. Solved problem.
* Topic:Socrates, Plato and Aristotle
* Introduction to Philosophy
# Observational astronomy

Astronomers can gain an understanding of objects in the universe by studying them with a telescope. Observational astronomy is the process of collecting and analyzing data to learn about these objects. In this learning project computer programs will be used to view and study images or measurements taken with a telescope to learn basic concepts in astronomy.

## Introduction

The activities in this learning project are based on the idea of learning by doing. You will learn about astronomy by going through the same process that an astronomer does to analyze data. As you follow the instructions in the activity you should also follow the links to related reading materials.

## Activities

Some activities require no more than the naked eye and a site where there are few nearby lights so the sky is reasonably dark at night. For some, a pair of binoculars or a small telescope will suffice. Other activities can be done with free computer software. However, some require more elaborate equipment.
* Meteor observing
* Image processing
* Supernova
* Extrasolar planet
* Variable stars
Visit the planning page to see some ideas on how this project might develop, and check back often to see the progress.

## Readings

Background information:
* Wikipedia:Observational astronomy
* Wikipedia:Telescope
# Bash programming/Note taking

This is a productivity shell script that can be used for note taking into a text file. It automatically applies time stamps before each line. The text file can later be edited using a text editor.
It can be used on both Linux (on desktop and laptop computers) and Android-based smartphones using a terminal emulator software like the one by Jack Palevich or Termux. On Android, it can be downloaded from third-party sources.
It requires at least Android 7.0 given that sed was not included in Android before. If compatibility with Android 6.0 is necessary, all | sed pipes need to be removed from the code. They are used to replace for a tab separated value (TSV) layout where a comma is substituted with an indent character and two commas are substituted with one comma. This functionality is unavailable prior to Android 7.
In addition to the main note file "N.txt", it creates a raw file called "N.raw.txt" which contains unmodified user input and "N.debug.txt" which contains more technical information.
For statistical use, it also memorizes a total line count into a text file called ".lnid" (line ID) and a session count into ".sid" (session ID). The window also shows a line counter of the number of lines of the current sessions (lnc).
# Euclidean vector space/Definition

A real, finite-dimensional vector space that is endowed with an inner product, is called an Euclidean vector space.
# MDLD/Euclidean space

Start=Euclidean space Target=Euclidean vector space/Definition
# MDLD/complex-conjugated

Start=complex-conjugated See=complex conjugation MDLD/complex conjugation Target=Complex numbers/Complex conjugation/Definition
# MDLD/inner product (R)

Start=inner product (R) Target=Vector space/K/Inner product/Definition
# MDLD/linear equation

Start=linear equation Target=System of linear equations/Set of variables/Homogeneous and inhomogeneous/Definition
# MDLD/direct sum

Start=direct sum Target=Vector space/Linear subspaces/Finite/Direct sum/Definition
# Vector space/K/Inner product/Orthogonal projection/Introduction/Section

For a finite-dimensional ${\mathbb {K} }$-vector space, endowed with an inner product, and a linear subspace $U\subseteq V$, there exists an orthogonal complement $U^{\perp }$, and the space has the direct sum decomposition
    $V=U\oplus U^{\perp }\,.$
The projection
    $p_{U}\colon V\longrightarrow U$
along $U^{\perp }$ is called the orthogonal projection onto $U$. This projection depends only on $U$, because the orthogonal complement is uniquely determined. Often, also the mapping $V\rightarrow U\rightarrow V$ is called the orthogonal projection onto $U$. An orthogonal projection is also described as dropping a perpendicular onto $U$.

## Lemma

Let $V$ be a finite-dimensional ${\mathbb {K} }$-vector space, endowed with an inner product, and let $U\subseteq V$ denote a linear subspace with an orthonormal basis $u_{1},\ldots ,u_{m}$ of $U$. Then the orthogonal projection onto $U$ is given by
    $p_{U}(v)=\sum _{i=1}^{m}\left\langle v,u_{i}\right\rangle u_{i}\,.$

### Proof

We extend the basis to an orthonormal basis $u_{1},\ldots ,u_{n}$ of $V$. The orthogonal complement of $U$ is
    $U^{\perp }=\langle u_{m+1},\ldots ,u_{n}\rangle \,.$
Due to fact, we have
    $v=\sum _{i=1}^{n}\left\langle v,u_{i}\right\rangle u_{i}={\left(\sum _{i=1}^{m}\left\langle v,u_{i}\right\rangle u_{i}\right)}+{\left(\sum _{i=m+1}^{n}\left\langle v,u_{i}\right\rangle u_{i}\right)}\,.$
Therefore, $\sum _{i=1}^{m}\left\langle v,u_{i}\right\rangle u_{i}$ is the projection onto $U$ along $U^{\perp }$.
$\Box$
# MDLD/modulus (K)

Start=modulus (K) Target=Complex numbers/Modulus/Definition
# MDLD/orthogonal (matrix)

Start=orthogonal (matrix) Target=Orthogonal matrix/Orthogonal group/Field/Definition
# MDLD/isometry (Euclidean)

Start=isometry (Euclidean) Target=Vector spaces/K/Inner product/Linear isometry/Definition
# MDLD/unitary (matrix)

Start=unitary (matrix) Target=Matrix/C/Unitary group/Definition
# MDLD/standard inner product (R)

Start=standard inner product (R) Target=R^n/Standard inner product/Example
# MDLD/eigenline

Start=eigenline See=eigenspace MDLD/eigenspace Target=Linear mapping/Eigenspace/Definition
# MDLD/proper linear isometry

Start=proper linear isometry Target=Euclidean vector space/Proper isometry/Definition
# MDLD/proper isometry

Start=proper isometry Target=Euclidean vector space/Proper isometry/Definition
# MDLD/improper (isometry)

Start=improper (isometry) Target=Euclidean vector space/Proper isometry/Definition
# MDLD/plane rotation

Start=plane rotation Target=Plane isometries/Section
# MDLD/infimum (R)

Start=infimum (R) Target=Real numbers/Subset/Infimum/Definition
# Inner product/K/Polarization identity with norm/Fact/Proof/Exercise

Let $V$ denote a vector space over ${\mathbb {K} }$, endowed with an inner product $\left\langle -,-\right\rangle$. Let $\Vert {-}\Vert$ denote the associated norm.
a) Show that, in the case ${\mathbb {K} }=\mathbb {R}$, the relation
    $\left\langle v,w\right\rangle ={\frac {1}{2}}{\left(\Vert {v+w}\Vert ^{2}-\Vert {v}\Vert ^{2}-\Vert {w}\Vert ^{2}\right)}\,$
holds.
b) Show that, in the case ${\mathbb {K} }=\mathbb {C}$, the relation
    $\left\langle v,w\right\rangle ={\frac {1}{4}}{\left(\Vert {v+w}\Vert ^{2}-\Vert {v-w}\Vert ^{2}+{\mathrm {i} }\Vert {v+{\mathrm {i} }w}\Vert ^{2}-{\mathrm {i} }\Vert {v-{\mathrm {i} }w}\Vert ^{2}\right)}\,$
holds.
# R^n/Standard inner product/Exercise

Show that the standard inner product on $\mathbb {R} ^{n}$ is indeed an inner product.
# Inner product/K/Linear subspace/Exercise

Let $V$ be a ${\mathbb {K} }$-vector space, endowed with an inner product $\left\langle -,-\right\rangle$, and let $U\subseteq V$ denote a linear subspace. Show that the restriction of the inner product to $U$ is again an inner product.
# Complex inner product/Real part/Inner product/Exercise

Let $V$ be a complex vector space, endowed with an inner product $\left\langle -,-\right\rangle$. Show that the real part of this inner product is an inner product on the underlying real vector space.
# Bilinear form/R^2/Computation/1/Exercise

Let $\left\langle -,-\right\rangle$ denote a bilinear form on $\mathbb {R} ^{2}$, with the values $\left\langle e_{1},e_{1}\right\rangle =5$, $\left\langle e_{1},e_{2}\right\rangle =-4$, $\left\langle e_{2},e_{1}\right\rangle =7$, and $\left\langle e_{2},e_{2}\right\rangle =-3$. Compute $\left\langle {\begin{pmatrix}3\\-4\end{pmatrix}},{\begin{pmatrix}-5\\-6\end{pmatrix}}\right\rangle$. Is it an inner product?
# Normed vector space/Metric space/Fact/Proof/Exercise

Show that a normed ${\mathbb {K} }$-vector space is via
    $d(u,v):=\Vert {u-v}\Vert \,$
also a metric space.
# Normed vector space/Metric space/Fact/Proof/Exercise/Solution

* We have $d{\left(u,v\right)}=\Vert {u-v}\Vert =0$ if and only if $u-v=0$, that is, $u=v$.
* We have
    ${\begin{aligned}d{\left(u,v\right)}&=\Vert {u-v}\Vert \\&=\Vert {-1(v-u)}\Vert \\&=\vert {-1}\vert \cdot \Vert {v-u}\Vert \\&=d{\left(v,u\right)}.\end{aligned}}$
* For arbitrary $w\in V$, we have, due to the definition of a norm
    ${\begin{aligned}d{\left(u,v\right)}&=\Vert {u-v}\Vert \\&\leq \Vert {u-w}\Vert +\Vert {w-v}\Vert \\&=d{\left(u,w\right)}+d{\left(w,v\right)}.\end{aligned}}$
# Learning resource

Learning resources are text, media, and other digital assets that are useful for teaching, learning, and assessing as well as for research purposes. Wikiversity has many types of learning resources not available at other Wikimedia Foundation projects (see: What Wikiversity is not). However, Wikiversity doesn't automatically include all of the learning resources available in other projects, such as encyclopedia articles, textbooks, or source texts (see: Wikimedia). In special cases these types of resources may be hosted by Wikiversity projects.

## What learning resources does Wikiversity include?

Wikiversity includes learning resources in all subject areas for all age groups. Learning resources can be roughly divided into:
* Learning projects that support active learning, and
* Static learning materials for use outside of Wikiversity.

### Learning projects

Learning projects guide active learners to exercises and collaborative learning projects. See: Portal:Learning Projects.

### Research projects

Research is an integral part of advanced education and professional work in many fields. See Wikiversity:Research for information on Wikiversity research projects.

### Learning materials

Learning materials can be audio and video files, text files and are generally static learning objects that can be used either by Wikiversity participants or downloaded for use at bricks-and-mortar educational institutions.

## Finding Wikiversity Learning resources

Portals. Every Wikiversity learning resource may be linked to by at least one portal page. You can browse the Wikiversity portals. See Category:Portals.
Categories. Every Wikiversity learning resource should be in at least one Category. You can browse Wikiversity by category. See: Category:Categories.
Search. Try using the search feature to find learning resources. See: Wikiversity:Searching.

### Your turn

Wikiversity had many learning resources that are on hard-to-find pages. You can help make sure that every learning resource has a link to it from at least one portal page. Particularly exciting learning resources should become featured content on portals or the Main Page.
When existing portals become too crowded you can make new portals.

## Creating learning resources

See: Wikiversity:Content development.
# Linear algebra (Osnabrück 2024-2025)/Complex inner product/Real part/Inner product/Exercise/Exercisereferencenumber

Exercise 31.3
# Vector space/C/Inner product/R/Norm/Exercise

Let $V$ be a complex vector space, endowed with an inner product $\left\langle -,-\right\rangle$. Show that the norm of this inner product coincides with the norm arising by considering $V$ as a real vector space, endowed with the corresponding real inner product.
# Linear algebra (Osnabrück 2024-2025)/Vector space/C/Inner product/R/Norm/Exercise/Exercisereferencenumber

Exercise 31.11
# Linear algebra (Osnabrück 2024-2025)/Inner product/K/Polarization identity with norm/Fact/Proof/Exercise/Exercisereferencenumber

Exercise 31.10
# Linear algebra (Osnabrück 2024-2025)/Normed vector space/Metric space/Fact/Proof/Exercise/Exercisereferencenumber

Exercise 31.17
# Inner product/R/Cauchy Schwarz/Equal and not/Exercise

Let $V$ be a real vector space, endowed with an inner product $\left\langle -,-\right\rangle$. Show that in the estimate
    $\vert {\left\langle v,w\right\rangle }\vert \leq \Vert {v}\Vert \cdot \Vert {w}\Vert \,$
of Cauchy-Schwarz, equality holds if and only if $v$ and $w$ are linearly dependent.
# Inner product/R/Cauchy-Schwarz/Fact

Vector space/R/Inner product/Norm/Situation
    $\vert {\left\langle v,w\right\rangle }\vert \leq \Vert {v}\Vert \cdot \Vert {w}\Vert \,$
for all
$v,w\in V$
# Linear algebra (Osnabrück 2024-2025)/Inner product/R/Cauchy Schwarz/Equal and not/Exercise/Exercisereferencenumber

Exercise 31.9
# Polynomials/Unit interval/2/Exercise

Let
    $f,g\colon [0,1]\longrightarrow \mathbb {R}$
be given by $f(x)=-x^{2}+1$, and $g(x)=x^{2}+x+3$. Compute $\left\langle f,g\right\rangle$ in the sense of example.
# Linear algebra (Osnabrück 2024-2025)/Continuous functions/Interval/C-valued/Inner product/Example/Examplereferencenumber

Example 31.6
# Polynomials/Unit interval/1/Exercise

Let
    $f,g\colon [0,1]\longrightarrow \mathbb {R}$
mit $f(x)=2x^{3}-x+3$ and $g(x)=-5x^{2}+4x-7$. Compute $\left\langle f,g\right\rangle$ in the sense of example.
# Inner product/R/Norm/Relation/Exercise

Let $V$ be a real vector space, endowed with an inner product $\left\langle -,-\right\rangle$. Confirm the identity
    $\Vert {x+y}\Vert ^{2}-\Vert {x-y}\Vert ^{2}=4\left\langle x,y\right\rangle \,.$
# R^n/v in unit ball and w normed/v+aw on boundary/Exercise

Let $v,w\in \mathbb {R} ^{n}$ be vectors fulfilling $\Vert {v}\Vert \leq 1$ and $\Vert {w}\Vert =1$. Show that there exists an $a\in \mathbb {R}$ such that $\Vert {v+aw}\Vert =1$ holds.
# Unit disk/n points/Exists point with distance at least n/Exercise

Let $n$ points $P_{1},P_{2},\ldots ,P_{n}$ in the unit disk $B$ be given, that is, $B={\left\{P\in \mathbb {R} ^{2}\mid d(P,0)\leq 1\right\}}$. Show that there exists a point $Q\in B$ fulfilling the property
    $\sum _{i=1}^{n}d(P_{i},Q)\geq n\,.$
# Euclidean vector spaces/Matrix space and trace/Exercise

Let $V=\operatorname {Mat} _{n}(\mathbb {R} )$. Show that $V$, endowed with the mapping
    $\left\langle -,-\right\rangle \colon V\times V\longrightarrow \mathbb {R} ,(A,B)\longmapsto \operatorname {trace} {\left(B^{t}A\right)},$
is a Euclidean vector space.
# Interval/Continuous functions/Equidistant subdivision/Properties of inner product/Limit/Exercise

Let $[a,b]$ be a closed real interval with $a<b$, and let $V={\left\{f:[a,b]\rightarrow \mathbb {R} \mid f{\text{ continuous}}\right\}}$. For $n\in \mathbb {N} _{+}$ and $f,g\in V$, let
    $\left\langle f,g\right\rangle _{n}:=\sum _{i=0}^{n}f{\left(a+i{\frac {b-a}{n}}\right)}g{\left(a+i{\frac {b-a}{n}}\right)}\,.$
What properties of an inner product
does $\left\langle -,-\right\rangle _{n}$ satisfy? What relation exists between $\left\langle -,-\right\rangle _{n}$ and the inner product from example?
# Inner product/Product space/Exercise

Let $(V_{1},\left\langle -,-\right\rangle _{1})$ and $(V_{2},\left\langle -,-\right\rangle _{2})$ be real vector spaces, endowed with inner products. Show that by
    $\left\langle (v_{1},v_{2}),(w_{1},w_{2})\right\rangle :=\left\langle v_{1},w_{1}\right\rangle _{1}+\left\langle v_{2},w_{2}\right\rangle _{2}\,,$
an inner product is defined on the product space $V_{1}\times V_{2}$.
# Inner product/K/Norm/Parallelogram law/Exercise

Let $V$ denote a vector space over ${\mathbb {K} }$, endowed with an inner product $\left\langle -,-\right\rangle$. Let $\Vert {-}\Vert$ denote the associated norm. Show that the so-called Parallelogram law holds, that is
    $\Vert {v+w}\Vert ^{2}+\Vert {v-w}\Vert ^{2}=2\Vert {v}\Vert ^{2}+2\Vert {w}\Vert ^{2}\,.$
# Maximum norm/Norm/Exercise

Show that the maximum norm on ${\mathbb {K} }^{n}$ is a norm.