OpenLLM-France/wikimedia huggingface dataset:
# Endomorphism/Jordan normal form/Introduction/Section
## Definition

Jordan matrix/Above/Definition
If we consider such a Jordan matrix as a linear mapping $\varphi$ on the standard space $K^{n}$, then
    $\varphi (e_{1})=\lambda e_{1}{\text{ and }}\varphi (e_{k})=\lambda e_{k}+e_{k-1}{\text{ for all }}k\geq 2.$
In particular, $e_{1}$ is a eigenvector to the eigenvalue $\lambda$. A simple observation shows that there is no further eigenvector linearly independent to $e_{1}$ (see exercise). The property on the right is equivalent with the condition
    $e_{k-1}=(\varphi -\lambda \cdot \operatorname {Id} )(e_{k})\,$
for $k\geq 2$. The eigenvector $e_{1}$ is a generating element of the kernel of the mapping $\psi :=\varphi -\lambda \operatorname {Id}$, and the other standard vectors $e_{k}$ arise successively as preimages of $e_{k-1}$ under $\psi$.

## Definition

Upper triangular matrix/Jordan normal matrix/Definition
The Jordan matrices occurring here are called the Jordan blocks of the matrix. Their eigenvalues might be different or equal. In the matrix
    ${\begin{pmatrix}2&1&0&0&0&0\\0&2&0&0&0&0\\0&0&4&1&0&0\\0&0&0&4&1&0\\0&0&0&0&4&0\\0&0&0&0&0&2\end{pmatrix}},$
there are three Jordan blocks,
    ${\begin{pmatrix}2&1\\0&2\end{pmatrix}},\,{\begin{pmatrix}4&1&0\\0&4&1\\0&0&4\end{pmatrix}}{\text{ and }}{\begin{pmatrix}2\end{pmatrix}}$
with eigenvalues $2,4$ and again $2$.
We state and prove now the theorem about the Jordan normal form for trigonalizable endomorphisms.

## Theorem
### Proof

$\Box$
Hence, every upper triangular matrix is similar to a matrix in Jordan normal form. Over the complex numbers, every matrix can be brought to Jordan normal form. If a matrix has Jordan normal form, then we can read of directly the diagonalizable and the nilpotent part in the sense of fact: The diagonal yields the diagonalizable part, and the entries which are strictly above the diagonal, yield the nilpotent part (in general, this is not true for upper triangular matrices).

## Example

* ↑ In the context of trigonalizable mappings and in order to find the Jordan normal form, it is useful to work with $\varphi -\lambda \cdot \operatorname {Id}$ instead of $\lambda \cdot \operatorname {Id} -\varphi$.
# African Philosophy/Annotated Bibliography/Claude Sumner The Source of African Philosophy the Ethiopian Philosophy of Man
## Bibliographical Information

Sumner, Claude:, The Source of African Philosophy: the Ethiopian Philosophy of Man, Aethiopistische Forschungen (Ed. Siegbert Uhlig), Vol. 20, 1986, Universität Hamburg, Abteilung Afrikanistik und Äthiopistik

## URL where reference was found

http://www1.uni-hamburg.de/AEF// - note web link for specific article does not exist, hardcopy only and not available online.

## Abstract

In-depth treatment of Ethiopian philosophy plus an anthology of several texts translated into English (from Ge'ez) by the author:
* Sections of "The Physiologue", "The book of Philosophers" and "The life and Maxims of Skendes"
these are translations into Ge'ez adapted or augmented by the translators to Ethiopian thinking. In that sense, they can be called "Ethiopian philosophy"
* "The treatise of Zera Yacob" (complete text)
* Parts of the "Treatise of Walda Heywat"
The latter two are original Ethiopian philosophy.
# African Philosophy/Annotated Bibliography/Kwasi Wiredu African Philosophical Tradition A Case Study of the Akan
## Bibliographical Information

Wiredu, Kwasi: African Philosophical Tradition: A Case Study of the Akan In: The Philosophical Forum, Vol. XXIV, No. 1-3, Fall-Spring, 1992-3, pp. 41 ff.
# African Philosophy/Annotated Bibliography/Kwasi Wiredu Toward Decolonizing African Philosophy And Religion
## Bibliographical Information

Wiredu, Kwasi: Toward Decolonizing African Philosophy And Religion In: African Studies Quarterly, The Online Journal for African Studies, Volume 1, Issue 4, 1998

## URL of Original Article

http://web.africa.ufl.edu/asq/v1/4/3.htm

## references/cites

Kwasi Wiredu African Philosophical Tradition A Case Study of the Akan
# African Philosophy/Annotated Bibliography/Paulin Hountondji African philosophy myth and reality
## Bibliographical Information

Paulin J. Hountondji: African philosophy: myth and reality, transl. by Henri Evans with the collab. of Jonathan Ree; introd. by Abiola Irele. - 2nd ed. - Bloomington [etc.]: Indiana University Press, cop. 1996. - XXVIII, 221 p. - Original edition: 1983. ISBN 0-253-33229-X ISBN 0-253-21096-8 pbk

## URL where reference was found

http://www.ascleiden.nl/Library/Webdossiers/AfricanPhilosophy.aspx -this is a dead link.
# African dance as proprioceptive art

The following is a research hypothesis derived from experience with learning African dances:
    African dance is essentially not a visual, but a proprioceptive art, i.e. an art form targeting the body-internal sensors (see Proprioception).
    A rhythmic pattern might be perceived as an auditive pattern (in the music one can here) or visual (in a dance one sees). From the point of view of the dancer, the same rhythmical pattern might also be a proprioceptive pattern, i.e. a pattern that the dancer observes with the muscle and touch receptors in his body. The abstract pattern is always the same. You can transfer a piece of music to another musical instrument or you can "play" it with your own body.
    So music in Africa is not necessarily an auditive art. In fact, African polycentric dance can be viewed as a proprioceptive art where the dancer is the only person who can perceive the piece of art completely. The rhythmical structure the dancer feels in the body is then integrated with the auditive music into a "multimedia" experience of great esthetic beauty. So Africans have created an art form for the body-internal proprioceptive senses which have been neglected in other parts of the world as a target for art.
    If one knows the dance, one can perceive the structures in somebody else's dance one observes, but primarily, African dance is not a visual art but a proprioceptive art. The fact that many African languages don't distinguish between concepts of music and dance in the same way as European languages do might therefore be based on the following phenomena: an auditive pattern might be transferred to a proprioceptive pattern and vice versa (the abstract pattern of "music/dance" being the same in both ways of performing it) and both parts of the experience might be integrated into one multimedia "gesamtkunstwerk" in the dancer's/listener's brain/mind.

## Questions

1) Has this hypothesis about African dance been formulated before? If so, relevant references should be posted here.
    The concept and general idea of the possibility of proprioceptive art appears, too, in Markus Schrenk's article ‘Is Proprioceptive Art Possible?’ (in Graham Priest and Damon Young (eds): Anthology on the Philosophy of Martial Arts. Routledge (2014) 101–116).
    Independently of this entry here, Schrenk argues that (some) Martial Arts can be subsumed under the category 'proprioceptive art'. The formulation "To play ones body as an instrument" can be found there too, and, also, the observation that, in proprioceptive art, the performer is (necessarily) their own audience.
    It is great so see that the concept of "proprioceptive art" finds its application also in African Dance!
2) How is dance and music conceptualized in African languages. Do these conceptualizations show a concept of proprioceptive music (music felt in the body instead of being heard).

## See Also

* Division of African Music and Dance
# African music and dance

Welcome to the Department of African Music and Dance, part of the School of Music and Dance and the School of African Studies.

## Division description

The scope of this division is
* to collect knowledge on African music and dance
* to develop teaching materials about African music and dance
* to develop research methods for the study of African dance
* to provide a scientific basis for the improvement of the coverage and quality of Wikipedia articles related to this subject.

## Research topics

* African dance as proprioceptive art

## Active participants

If you would like to contribute to this, please add a reference to your user page here.
* User:Nannus
# Afrikaans

Afrikaans is a Germanic language closely related to Dutch and is spoken in Southern Africa in the Republic of South Africa and Namibia. The language stems from 17th century Dutch and has been influenced by local African languages as well as languages spoken by other immigrants to the 17th century Cape region - German, French and Malay.
Are you traveling to South Africa? Well, Afrikaans is one of the languages of South Africa. If you know Dutch, you won't have a hard time learning Afrikaans. Even if you're English, Afrikaans won't be hard! Good luck!

## Lessons

* Pronunciation
* Alphabet
* Greetings
* Tenses
* Vocabulary

## See Also

* Wikipedia: Afrikaans
* Afrikaans Wikipedia
* Afrikaans Wiktionary
# Afrikaans/Greetings

Hallo (hah-low) - Hello Goeiedag (gwee-uh-dach) - Good day Goeiemiddag (gwee-uh-muh-dach) - Good afternoon Goeienaand (gwee-uh-naand) - Good evening
Hoe gaan dit? (hoo gahn duht) - How are you? Goed, en met jou? (goot ehn meht yoe) - Fine, and you? Goed dankie (goot dung-key) - Fine thanks.
My naam is ... (may nahm uhs ...) - My name is ...
Asseblief (ah-suh-bleef) - Please Dankie (dung-key) - Thank you
# Afrikaans/Alphabet

A Short (A) Long (AA)
B Similar to English
C Either S or K, e.g. SirKel
D Similar to English
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Short (A) Long (AA) Similar to English Two sound possible, soft and gutteral Similar to English Short (I) Long (IE), and not (II) Like English Y, e.g. JES(afr) = YES(eng) Similar to English Similar to English Similar to English Similar to English Short (O) Long (OO) Similar to English KW used, eg. KWART = 1/4 Similar to Spanish Similar to English Similar to English Short (U) Long (UU) Similar to English F Unique sound Used in loan words only Like English "ay" e.g. YL(afr) = ALE (eng) S is often used
Similar to English Either S or K, e.g. SirKel Similar to English Short (A) Long (AA) Similar to English Two sound possible, soft and gutteral Similar to English Short (I) Long (IE), and not (II) Like English Y, e.g. JES(afr) = YES(eng) Similar to English Similar to English Similar to English Similar to English Short (O) Long (OO) Similar to English KW used, eg. KWART = 1/4 Similar to Spanish Similar to English Similar to English Short (U) Long (UU) Similar to English F Unique sound Used in loan words only Like English "ay" e.g. YL(afr) = ALE (eng) S is often used
# Afrikaans/Pronunciation
## Pronunciation Guide

a - as u in cup (kap) aa - as u in cup but longer like ah (daad) aai - as y in why (laai) ae - as u in dust but longer like ah, followed by article a (dae) b - similar to b in English c - as k in kitten (Calvinis) c - as s in size (celcius) ch - guttural sound like ch in loch (chemie) ch - as k in kitten (chloor) ch/sj - as sh in shot (China/Sjina) d - as d in donkey (daar) d - as t in hat (bed) e - as ee in deer (edel) e - as e in hen (ken) e - as e in angel (bevat) ê - as ai in hair (hê) ee - as ee in deer (een) eë/ië - as ea in fear, pronounced as two sounds (leër/skiër) eeu - as ew in few (leeu) ei - as ay in play (seil) eu - as ee in deer with lips pouted (deur) eu - as ew in few (euforie) f - similar to f in English g - gutteral sound like ch in loch (geld) gh - as g in golf (gholf) h - similar to h in English i - as e in angel (sit) ie - as ee in breed (dier) ie - as i in sick (siek) j - as y in you (jaar) kn - as c in cat + n in no (knoop) ng - as ng in sing (vang) o - as oo in loot followed by rapid w with pouted lips (bode) o - as oo in loot, but shorter (euforie) o - as o in fort but shorter (oggend) o - as oy in boy (potjie) ô - as au in cause (môre) oe - as oo in loot (voer) oe - as oo in loot, but shorter (voet) oë - as oe in doer (vermoë) oei - as ooey in phooey but preceded with rapid w (koei) oo - as oo in loot followed by rapid w with pouted lips (soom) ooi - as oi in oil but preceded with rapid w (strooi) ou - as oa in coat (hout) p - similar to p in English r - as r in very, but lightly rolled (duiker) r - strongly rolled r, almost Scots (rooi) s - similar to s in English t - similar to t in English tj - as ch in chunk (tjank) u - as i in sick with lips pouted (u) ui - as ay in play but longer with pouted lips (lui) uie - as aye in player but longer with pouted lips (beduie) uu - as ee in breed but with lips pouted (duur) v - as f in fun (vul) w - as w in sweep (swem) w - as v in visit (water) y - as ay in play (yster)
z - similar to z in English
# Catalogue 22/Site Office - A. Thomas

Part of Catalogue 22, Catalogue 22 on Google Maps
Designer: Amanda Thomas Degree: M. Architecture School: Carleton University Year: 2011 Location of Project: Wellington Street and Bank Street
Project Status: Unbuilt
Project required to accommodate four workstations, drawing viewing spaces, and a boardroom component for project meetings. This involved the renovation of an existing, unoccupied space to accommodate a site office for the construction phase of the wellington building renovation.
# Catalogue 22/San Gimigiano Tower - S. Wolba

Part of Catalogue 22, Catalogue 22 on Google Maps
Designer: Stephen Wolba Degree: B. Architecture School: Carleton University Year: 2009 Location of Project: San Gimignano, Italy
Project Status: Unbuilt
Inspired by the vineyards that surround the small Italian town of San Gimignano, this experiential observation tower draws the viewer in through a small clearing in its “vines” and directs them up the tower. During their ascent, they are given slight glimpses to the exterior, before reaching the middle observation decks where they can observe the city as a whole from above. As they finally reach the top, their experience flourishes as they are gracefully presented with the top observation deck. Here they receive an unobstructed view of both the city and the surrounding vineyards, and are able to observe how the two weave together and intertwine.
# Catalogue 22/Shelt-a-Wé, a shelter away from home

Part of Catalogue 22, Catalogue 22 on Google Maps
Designer: Warren Borg Degree: B. Architecture School: Ryerson University Year: 2008 Location of Project: Ryerson University Campus
Project Status: Built
The "Shelt-a-Wé" has a unique shape and look, not seen in other picnic shelters, which can benefit the occupant in more ways than one. Its sloping roof can deflect the rain, snow, wind, or even sunlight. Its sloping trusses are used to maximize lateral support, limiting the use of tension cables or deep footings, enabling it to be a mobile structure. This design is to simplify the construction process for students as the primary builders
# Catalogue 22/Smith House Plan

Part of Catalogue 22, Catalogue 22 on Google Maps
Designer: Jaclyn Squizzato Degree: B. Architecture School: Carleton University Year: 2008 Location of Project: West Vancouver, B.C.
Project Status: Unbuilt
Analysis of the Smith House architecture and construction methods. Specific focus on Japanese wood joinery and heavy timber construction.
# Catalogue 22/Solar Decathalon - A. Thomas

Part of Catalogue 22, Catalogue 22 on Google Maps
Designer: Amanda Thomas Degree: B. Architecture School: Carleton University Year: 2010 Location of Project: Carleton University
Project Status: Unbuilt
The concept for the design is light as a guide through one’s day, further expressed by using the axis of the compass as an organizational tool for dividing space. The design team comprised of engineers, architects working together to create a net zero solar inspired house for the 2011 competition, with the intention to construct at full scale 2012.
# Catalogue 22/The Elephant and the Butterfly

Part of Catalogue 22, Catalogue 22 on Google Maps
Designer: Chris Cormier, Chrissy Taylor and Jessica Hickling
Degree: M. Architecture
School: Carleton University
Year: 2012
Project Location: Cleveland, OH
Project Status: Unbuilt
Car horns, exhaust, slamming doors, the low frequency waves of a car stereo wash over your body. The urban chaos immersing you is so familiar that it takes some time before you realize that today something is different. Something unknown is emerging on the horizon, tangible only in the periphery; you occupy the moment between when a presence is felt behind you and when they announce themselves. All senses at attention, your ears straining against the traffic and the wind and that is when realization hits: it is not wind but a breeze is rustling the trees.
As the traffic beside you falls away, relegated to the underworld, the cityscape beneath your feet transforms and gives way to nature. You revel in the spectacle laid before you: a space of chance and magic within the city. Each person becomes part of the larger performance; Banker, daredevil, teacher and ballerina alike. This forest, new but strangely familiar, stands among landmarks you have known for years but are now seeing again for the first time. The very city that surrounds you seems to sit in waiting, reinvigorated and open to the same possibility.
# Catalogue 22/Reading Room - Introduction to Architectural Technology

Part of Catalogue 22, Catalogue 22 on Google Maps
Designer: Jaclyn Squizzato Degree: B. Architecture School: Carleton University Year: 2008 Location of Project: Carleton University, Ottawa
Project Status: Built
The objective of the project was to explore the building process through a series of physical construction phrases which resulted in an addition to an undetermined pre-existing structure. All materials and construction details were left up to the students who worked in pairs. My partner and I chose to utilize a light gauge steel frame construction, with a concrete foundation, and wood paneling to clad and insulate. Two small windows at the front end of the structure provide ample light for reading and the high ceiling entry space which projects a grand atmosphere, quickly narrows into a private reading nook next to the windows.
# Catalogue 22/Rotating Tower

Part of Catalogue 22, Catalogue 22 on Google Maps
Designer: Jaclyn Squizzato Degree: B. Architecture School: Carleton University Year: 2008 Location of Project: Carleton University, Ottawa
Project Status: Unbuilt
Each student was assigned to physically construct the architectural manifestation of one chapter from "Invisible Cities" by Italo Calvino. The city which inspired this project was one in which the past, present, and future all existed concurrently. In order to give physical form to this extremely conceptual program, I designed a tower in which each level rotated according to the speed of the winds. Materiality influenced the design as heavier materials were placed lower to the ground, thereby have less exposure to wind and rotating at paces of centuries. Contrastingly, lighter metal construction which would be placed closest to the top of the structure would rotate at a daily pace. In this way an individual approaching the structure would be able to view the passage of time through the decay of different materials and the rotation of the tower. Each viewing would therefore become predictable to some degree, and entirely unpredictable in others.
# Catalogue 22/San Gimigiano Tower - J. Squizzato

Part of Catalogue 22, Catalogue 22 on Google Maps
Designer: Jaclyn Squizzato Degree: B. Architecture School: Carleton University Year: 2009 Location of Project: San Gimignano, Italy
Project Status: Unbuilt
San Gimignano Tower which used traditional construction materials from the historical city. Tower loosely based on the forms of Renzo Piano's Jean Marie Tjibaou Cultural Center.
# Catalogue 22/San Gimignano Tower - J. Hickling

Part of Catalogue 22, Catalogue 22 on Google Maps
Designer: Jessica Hickling Degree: B. Architecture School: Carleton University Year: 2009 Location of Project: San Gimignano, Italy
Project Status: Unbuilt
The task was to create a tower in the ancient city of San Gimignano, Italy and keep in mind the relation it will have to the existing urban area. The tower engages the public by its light steel frame and glass structure. As the tower is ascended, one passes through two existing towers and may view their rich history on a closer level. Finally one reaches the top arriving at a view of the city and surrounding vast fields. Upon descent from the tower the view of the city unfolds through the glass panels of the roof structure.
# BCP/Sorbus americana

Sorbus americana
| Wikipedia • Commons • Wikibooks (horticulture) • Wikibooks (subject) • Wikispecies • Fruit and seed clock | Profile for Sorbus americana (American Mountain Ash) Identifying Characteristics Habit:TreeFlowers:Perfect, white, one-eighth of an inch across, borne in flat compound cymes three or four inches across. Bracts and bractlets acute, minute, caducous.Foliage:Alternate, compound, unequally pinnate, six to ten inches long, with slender, grooved, dark green or red petiole. Leaflets thirteen to seventeen, lanceolate or long oval, two to three inches long, one-half to two-thirds broad, unequally wedge-shaped or rounded at base, serrate, acuminate, sessile, the terminal one sometimes borne on a stalk half an inch long, feather-veined, midrib prominent beneath, grooved above. They come out of the bud downy, conduplicate; when full grown are smooth, dark yellow green above and paler beneath. In autumn they turn a clear yellow. Stipules leaf-like, caducous.Stem:Bark is light gray, smooth, surface scaly. Branchlets downy at first, later become smooth, brown tinged with red, lenticular, finally they become darker and the papery outer layer becomes easily separable.Fruit:Berry-like pome, globular, one-quarter of an inch across, bright red, borne in cymous clusters. Ripens in October and remains on the tree all winter. Flesh thin and sour, charged with malic acid; seeds light brown, oblong, compressed; cotyledons fleshy.Life Cycle: PerennialSimilar Plants:Sorbus aucuparia Recent Logs Jomegat 12:13, 4 May 2010 (UTC) (view all logs) |
Global data:
Regional data: New Hampshire: May, June
Additional images:
# BCP/Spergularia

Spergularia
| Wikipedia • Commons • Wikibooks (horticulture) • Wikibooks (subject) • Wikispecies • Fruit and seed clock | Profile for Spergularia (Sandspurry) Identifying Characteristics Habit:Herbaceous forbFlowers:Five purple petals with sepals between each. Yellow anthers. Blossoms are about 8 mm across.Foliage:Needle-like leaves form in whorls about the stem.Stem:Round, creeping stems have a reddish tint.Growing Conditions:Waste placesLife Cycle: Annual/Perennial Recent Logs Jomegat 23:23, 5 May 2010 (UTC) (view all logs) |
Global data: Temperate zone season(s): Late Spring, Early Summer, Mid Summer, Late Summer, Early Fall
Regional data: New Hampshire: May, June, July, August , September
Additional images: