Reflections, orthogonal and symplectic
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Formal Metadata
Title 
Reflections, orthogonal and symplectic

Title of Series  
Number of Parts 
6

Author 

License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
Identifiers 

Publisher 
Institut des Hautes Études Scientifiques (IHÉS)

Release Date 
2013

Language 
English

Content Metadata
Subject Area 
00:00
Group action
Theory of relativity
Diagonal
Generating set of a group
Reflection (mathematics)
Direction (geometry)
Element (mathematics)
Division (mathematics)
Group action
Mereology
Rule of inference
Food energy
Number
Connected space
Meeting/Interview
Lecture/Conference
Helmholtz decomposition
Film editing
Symmetric matrix
Position operator
02:49
Group action
Multiplication sign
1 (number)
Sheaf (mathematics)
Insertion loss
Complete metric space
Mereology
Subset
Maxima and minima
Sign (mathematics)
Plane (geometry)
Matrix (mathematics)
Analogy
Negative number
Monster group
Position operator
Covering space
Spacetime
Theory of relativity
Octahedron
Product (category theory)
Reflection (mathematics)
Gradient
Coordinate system
Bilinear form
Metric tensor
10 (number)
Recurrence relation
Flow separation
Category of being
Angle
Vector space
Triangle
Uniform space
Resultant
Relief
Geometry
Threedimensional space
Existence
Divisor
Cone penetration test
Connectivity (graph theory)
Real number
Similarity (geometry)
Routing
Student's ttest
Rule of inference
Open set
Wave packet
Number
Goodness of fit
Linear independence
Root
Wellformed formula
Operator (mathematics)
Green's function
Energy level
Integer
Symmetric matrix
Condition number
Shift operator
Kälteerzeugung
Element (mathematics)
Projective plane
Independence (probability theory)
Set (mathematics)
Cartesian coordinate system
Local Group
Field extension
Voting
Commutator
Film editing
9 (number)
Separation axiom
18:40
Lecture/Conference
Natural number
Reflection (mathematics)
Bilinear form
20:00
Threedimensional space
Presentation of a group
Transformation (genetics)
Mereology
Distance
Subset
Prime ideal
Plane (geometry)
Thermodynamisches System
Helmholtz decomposition
Wellformed formula
Symmetric matrix
Position operator
Covering space
Theory of relativity
Consistency
Forcing (mathematics)
Algebraic structure
3 (number)
Bilinear form
Local Group
Connected space
Metric tensor
Category of being
Graph coloring
Triangle
Object (grammar)
Game theory
Film editing
Fundamental theorem of algebra
Resultant
Directed graph
00:03
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00:17
a The I think you're enters mentions its reflection sexually it's not it's all Olson insults yeah not really the connections yet so speak about the the the courage the most along this double has to the left direct effect of harassing can now so I will speak about most alone contribution of victory customers Maddox cuts algebra and as cuts which other rules that have a real divide my my best score on 2 parts of the article part and another listen plastic parts saw owned you stop this generalized parttime Maddox said symmetric energy from hydrogen bond going on and are Richard integers diagonal elements to and stop over diagonal elements to be among positive and assumes that the singer traceable send that message was released by the Hong Kong numbers DID Shostak a positive effect Hinduism into being to gestures such as Dubai AIG is concluded G PG I thought was sector it's symmetric matrix then and a remarkable such cut Magic's as it cuts would algebra the several version I will speak about it I think it's a minimal 1 people have merit some decomposition not all them floor Crandall diagonal inches up a critical parts His generators the apply each side if I enter a relations which now think most missile magician or that he
02:49
I have duly did actually page by page the these aging injury harmony and Jr clinched I was aware of the and to find this page the jury and then you also need relations suppose the essence of like by the JI commuter trains and that the type of foreign want was injured by the you will have to clean the letter and the state's similar for however doesn't quite come some miracles lists of relations in what is nice about this relations this so this level consists of 2 parts and consist of Evan coordinators of age consist of ancient and consists completion of EU and algebra is is the operator and at the end of rules it is the ah they should be go to respond to Monterville great components and a set of rules it has a falling currency remarkable property trust properties set before us contains all mean what's called Moon plusminus B I thought it that I thought I fight I'll fly out new based elements in accordance space there which should be a great comes gradients of elements you and their adviser green in mind said Pfizer Inc of millions of mines in the city and the set for and also contains 0 because it contains a gain of positive stance was and severity the whereabouts of their own the requisite positive about 2nd the centerfolds it's kind of a Walters a default is up about as subtle fruit contained Margaret from 0 it is front is contained in the Union of the Chambas Cplus students in the recent losses for the instruments is that sits contains a in the Union of positive and negative factor and 2nd in instead of property at all as a set of rules is invariant under that on this amendment and what is when growth is a simple generated by elections namely the reflections and the reflections of reflection by both of use of fight is and for elections 5 had forgeries these Alfred J. my apparently tens of the inspector can go right here for a drink from genomic although I but for Jacob divides the same because of that elements of due not and you see that that's it's really surprising because I'm in it a such that exists there is a minimal set that you can take a peripheral if its citizens property Texas that befall a base that was his plusminus confusion as analysts not to recruit make reflection that was as good as the Commission why all the elements like all always think positive or negative outcome it's kind of a miracle and is only provisional forwards existence of course algebras maybe we can make a lamentable which it be very complicated David wanted to convey treat and special small cases some large cases and completely scripted different techniques that sets a font of remarkable dramatic cholera all of the would onerous and atrocity will introduce real numbers science or integer numbers signs and all that as words it's just rock that I want to say that it's the this affliction belongs to a gym last likeness on the streets of this reflection belongs to this shift at their disposal to deficiency and knowledge of draw some basic example and then are is a potent tool because the opposite of the end simplest interest in government checks the no well 43 ended up sixfold this is hosted some positive and negative the Senate can make slick more complicated metrics so I didn't get a called fine algebra the set of all rules it's successfully true but it's a it's an integer that was like a super alliance and again at the consist of positive and negative about and can make even more complicated think which is a relief the algebra and love some Roach received money but a pictures like this you get Victrola let's say 1 0 then get triple its pursue 1 them somewhere else it's real and so on contribution summary here that's so adept the deposition obtained by reflection of a simple rules solicitors ends up in between you get an angle sector this squirrel it's 3 plusminus clerical 5 0 0 2 not to dangle sectors and everywhere and sends out what's called imagine rules the Zsigmond benighted form arguing with metrics exists on Meggett element not positive under and real rules switcher democrats people think what he said that as this
10:45
kind of part of which is missed you spot of hyperbolic barely algebra and finally went and try to draw solace threedimensional example for example from semantic metrics like this on the set of rules will be a collection of reticence threedimensional space and you can project project do as at the take positive fruits and a that's a subset of Triangle and subset of triangles pretty complicated there seems somewhat you want me to be chose subset it's slipped through .period it's it's it's really some complicated product monster it produces and upbeat too the Nestle that's generous is a picture of this Starring and I'll call and get their formerly this property what those 3 geometrical support on that route groups some root rectal spaces not degenerate the simplistic symmetric farms on this some number let me the ledgers and other Runkle entourage get collection of letters look at plenary independent actress such it's still a problem between on fulltime drink nobody that is a symmetric matrix I In year just extent over the summer lotus space to make and there's a property Qantas recurrent is a fulllength those deserves is a subset baubles sitting came around with a falling to promptly following 3 properties the analog of property while old 1 promise that action would fill this that will be union over a rapper planes separable bolts did just that the replacement was back at planes all right all in all right so the 1st property if it is at set of walls campaigns union of quadrant cover planes all of its contains union of 2nd property said that the set of a complement to the walls contains a street positive Oct dance so 2 and it holds 6 seats in the blast the unity to the Niners the plaster is inevitable said the fall said it 3 or 4 times Iestyn composers all right tightens the minuses company said complaints but simplicial open simplicial cones it's a property is the same as it's a set of false is invariant under section of the value of this reflection walking noble to simplistic version Bloomberg dozens of elected populist voters related to cholesterol giraffes and other forms of Muskie so I stopped with pregame matrix with integer proficiency but now and I don't elements as you and it's it's magic accusing address below condition science look at the DIA where we don't know what is analog of cuts would algebra but there is a dramatic results will be very similar the the 1st of all those no rateable group Red Group in this case Bloomberg I sought to fully what what good Wilson Iowa you should go to a can of Alekos a geometric refrigeration and air a local dramatic reformulation is a full such as crafted defense emotional moon invitation simple that have vector space now will be the onedimensional Miss skews symmetric was on skis symmetric form market and have a collection of linearly independent directors interceptor space and Lille the relation is this numbers a jaded Beijing is positive comments :colon probably smart In the items in jail and I'm not I wanted to to find notion of irritation the imitation until the operation which met from 1 collection a new collection of actress the other 4 I prompt it is minus unfair I like it the symmetric case and Alfred J. Brian the use of forgery blasts and for Alfred J. divided by spent here to bless but what does it mean plus or 6 losses maxims of extensive on its it's essentially the same formula 1 can replace air Jaber was the same restaurant now this informal and also belongs to preparedness
18:42
some positive integers chief before I thought I would go so far all women and so that's how dramatically Assistance Mission looks like so we consider its copper plant life and and to get to provided for height this coverup plan because it's simplistic form and then there are some very in all collections which are on 1 side to preferably in the hands of his the pinnacles and Oscar Porter was unfair and another on the on the opposite side and the new collection is a fulllength remake minus 5 5 3 kids the same on 1 side and on the other side to be to them in directional previous original and fight that's and the look of this reflection notes informally dissing so it'll be completely indistinguishable and now well just the make completely
20:02
symmetric I don't want no can make for the History Channel Donald is a fulllength it should make analytical This Property Is there exists a subset the government was such that sitting out there and is a falling property so they know and local a swamp distributor will formally dramatic property with upandcoming sudden subset reach played its contain contains union of secure approval copper planes as a complement to the wall the campaigns against the in the might still do exactly the same as a new note in a form that contains 2 0 0 2 calls and instead of variants on the wound the glad groups will be different I wrote a formal letter accuses transformation we should it was called TI Alfred prime dismisses senior transformational Austin political prospects and the formula instead of fundamentals prolonged under the regular ride which will be replaced by the following it was at work before applying before making mutation all collection it will be the same as this transformation a plant was a wall of the original collection so if you make mutation makes the same picture but no not of linear force which after assessing the transformation assets this year amount 1 can make completely parolees for example of his business use the usual Elder Russell again is trying to get we can make this and so is is above knowledge of all 4 5 Wallstreet show 5 races most 6 threes but 5 races similarly for you to understand you won't get almost same picture as news of the interlopers the consideration of passing through kind of 2 negatively sector and positive part of also would you not worlds and inconsistent algebra and sperm and semen was used to be my 1 get since same picture but game was 1 of the big due to negative researchers aren't the same picture the same thing slope in the opposite and also there's someone has threedimensional version folk adventure of for example calculated example for this picture for the on this case and get extremely complicated decomposition color in small triangles have to produce additional protective so that's but know is that this is the price increasing story and a solid benefited them from data released it will more was the same way as that have only want brought for this result it falls on me some help caustic formalist and some In no some decomposition of filaments is simply Tom office group so it has nothing to do with cuts would allow algebra yes so here we have no idea how to make a joint simultaneous brought in there is some special case my metastasized midpriced symmetric it also gives him a chance and then there was some categories Suria don't suppose environs 1 can see someone knowledge interrelations input on the same footing but in general cases completely different than thinkin distance quit because there is so much of their should find some algebraic structures thank you on a question of course is to invite him with a generator for the launch of the Islamist and other than I used to go out and was questioned about because right group does exist and metrics assaults schism addressable yesterday the source and present Parsons is submitted should he you said where he was concerned July the connection with the Securities and Futures relations which the donation with affiliation with the help of the procure consider some kind of very well secret use of military uh 0 elected cover work could from the general workers would allows which related to his innocence of some will have a couple more for courses but bosom most of them are completely wealth objects have so it's the same thing here don't not although some baby baby CDU whatever it is in London the question the future hung