
herman grassman

herman gunthar grassman (,; 15 epril 1809-26 septambar 1877) addehathinte kaalath oru bhaashaashaasthranjanaayum ippol oru ganithashaasthranjanaayum ariyappettirunna oru jarmman bahushaasthranjanaayirunnu. addeham oru bhauthikashaasthranjanum, pothupanditanum, prasadhakanum koodiyaayirunnu. arupathukalil athunnathuvare addehathinte ganithashaasthra pravartthanangal valare kuravaayirunnu. addehathinte pravartthanangal ippol vekttar space ennariyappedunna aashayathin munbum athinumappuravum aayirunnu. n"-dimensional vekttar space "v"-nte ellah "k"-dimensional leanier subspaceukale paaraameettar cheiyunna space enna grassmenian addeham avatharippichu.
jeevacharitram.
herman vidyaabhyaasam nediya stettin jimneshyathil ganithavum bhauthikashaasthravum padippicha niyukta mantriyaaya justus gunder graasmaante 12 makkalil moonnaamanaayirunnu herman grassman.
prussian sarvakalaashaalakalilekkulla praveshana pareekshayil uyarnna maarkk nedunnathuvare oru vishishta vidyaarthiyaayirunnu grassman. 1827 muthal addeham berlin sarvakalashaalayil daivashaasthram padikkukayum classical bhashakal, thathwachintha, saahityam ennivayilum klaasukal edukkukayum cheythu. addeham ganithatthilo bhauthikashaasthrathilo kozhsukal eduthathaayi thonnunnilla.
ganithashaasthrathil sarvakalashala pariseelanam illengilum, 1830-ll berlinil patanam poortthiyaakkiya sesham stettinilekku madangiyethiyappol addehathinu ettavum thaalpparyamulla mekhalayaayirunnu athu. oru varshathe thayyaareduppinushesham, oru jimneshyathil ganithashaasthram padippikkaan aavashyamaaya pareekshakalil addeham pankedutthuvenkilum thaazhnna thalangalil maathram padippikkaan anuvadikkunnathra mikacha phalam nedi. eee samayathaan addeham thante aadyathe supradhana ganithashaasthra kandethalukal nadathiyathu, avaa 1844-leeii thante prabandhamaaya "dye lainale osdehangslehre, ainn neuer sweig derr maathamaattikk" ll addeham munnottuvacha pradhana aashayangalilekku addehathe nayichu, ivide eiii 1 ennu paraamarsikkunnu, pinneedu 1862-ll "dye osdehangslehre volstaandig undu inn strencher phoom bearbeat" ennu parishkarichu, ivide eiii 2 ennu paraamarsikkunnu.
1834-ll grassman berlinile geverbeshuleyil ganithashaasthram padippikkaan thudangi. oru varshathinusesham, ganithashaasthram, bhauthikashaasthram, jarmman, laattin, mathapadanam enniva padippikkunnathinaayi addeham stettinilekku madangi. adutha naalu varshathinullil, ellah secondary school thalangalilum ganitham, bhauthikashaasthram, rasathanthram, dhaathushaasthram enniva padippikkaan grassman pareekshayil vijayichu.
1847ll addehathe "oberlehrer" allengil pradhana adhyapakanaakki. 1852-ll stettin jimneshyathile antharicha pithaavinte sthaanathekku addeham niyamikkappedukayum athuvazhi professor enna padavi nedukayum cheythu. 1847ll addeham prussian vidyaabhyaasa manthraalayathodu oru sarvakalashaala sthaanathekku pariganikkaan aavasyappettu, thudarnnu aaa mantraalayam ernst kammarodu grasmanekkurichulla addehathinte abhiprayam chodichu. graasmante 1846 leeii sammana lekhanathil (chuvade kaanuka) "aparyapthamaaya roopathil prakadippicha prashamsaneeyamaaya nalla metteeriyal" adangiyirikkunnuvennu kumar thirichadichu."kammirinte report oru sarvakalashaala tasthika nedaanulla eathoru saadhyathayum avasaanippichu. eee episode maanadandam theliyichu; veendum veendum, grassmans dinathile pramukha vyakthikalkk addehathinte ganithashaasthrathinte moolyam thirichariyaan kazhinjilla.
germmaniyile rashtreeya prakshubdhathayude samayat, herman sahodaran robert chernnu oru bharanaghadanaaparamaaya raajavaazhchaykk keezhil jarmman ekeekaranathinu ahvaanam cheythukondu "dushe vochenshrift phur staatt, kirshe undu volksleban" enna stettin pathram prasidheekarichu. (ithu 1871-ll sambhavichu.) bharanaghadanaa niyamathekkurichu niravadhi lekhanangal ezhuthiya sesham, herman pathravumayi bandham verpeduthi, athinte rashtreeya dishayumaayi kooduthal kooduthal vairudhyamundennu kandethi.
grassman pathinonnu kuttikalundaayirunnu, avaril ezhu perr praayapoorthiyaayavaraayirunnu. oru makanaaya herman ernst grassman geisen sarvakalashaalayil ganithashaasthra professoraayi.
ganithashaasthranjan.
grassman irunna niravadhi pareekshakalilonnil veliyetta sidhaanthathekkurichu oru lekhanam samarppikkendathundu. 1840-ll addeham angane cheythu, laaplesinte "trettu dii mechanical seleste" yill ninnum lagranchinte "mechanical analytic" yill ninnum adisthaana sidhaantham eduthukondu, ennaal 1832 muthal addeham pariganichukondirunna vekttar reethikal upayogichu eee sidhaantham thurannukaattunnu. 1894-1911-nte "shekharicha kruthikalil" aadyamaayi prasidheekaricha eee lekhanathil ippol leanier aljibra ennu vilikkappedunnathinte aadya roopavum vekttar space enna ashayavum adangiyirikkunnu. addeham aaa reethikal thante "dye lainale osdehangslehre, ainn neuer sweig derr maathamettik" (eiii1), athinte pilkkala punaravalokanam "dye osdehangslehre volstaandig undu inn strencher phoom bearbeat" (eiii2) ennivayil vikasippichu.
1844-ll, grassman "osdehangslehre" ennu saadhaaranayaayi ariyappedunna thante maastarpees (eiii 1) prasidheekarichu, ithu "vipuleekarana sidhaantham" allengil "vipulamaaya vyaapthiyude sidhaantham" ennu vivarthanam cheiyunnu. ellah ganithashaasthrathinum oru puthiya adithara nirddeshichathinaal, daarshanika swabhaavathinte pothuvaaya nirvachanangalodeyaanu eee kruthi aarambhichath. thaan vaadicha beejaganita roopathilekku jyamiti cherthukazhinjaal, moonnaam nambarinu speshyal alavukalude ennamenna nilayil prathyeka punk illennu grassman pinneedu kaanichu; saadhyamaaya alavukalude ennam vaasthavathil paridhiyillaathathaanu.
fairenly-sander graasmaante rekheeya beejaganithatthinte aditharaye inipparayunna reethiyil vivarikkunnu
grassmente pithaavinekkurichulla oru ashayathe pinthudarnnu, eiii1, ippol baahya beejaganitam ennu vilikkappedunna oru beejaganithatthinte pradhana pravarthanamaaya "kompinettoriyal prodakt" (jarmman bhashayil "combinatorisches prodakt" allengil "auseras prodakt" "outtar prodakt") ennum vilikkappedunna baahya uthppannatheyum nirvachichu. (graasmaante kaalath, euclidean jyamithiyaayirunnu eaka svayamsidha sidhaanthamennum amoortha beejaganithathekkurichulla pothuvaaya ashayam ithuvare nirvachikkappettittilne oraal oormmikkanam.) 1878-ll, vilyam kingdon clifford eee baahya beejaganithathil vilyam rowan haamilttante kwaatterniyanukalumaayi chernnu, graasmaante niyamam "eppep" = 0-neey "eppep" = 1 enna niyamam upayogichu maatti. (kwaatterniyanukalkku, namukk "i" 2 = "j" 2 = "k" 2 = −1 enna niyamam undu.) kooduthal vishadaamshangalkku, baahya beejaganitam kaanuka.
a1 oru viplavakaramaaya grandhamaayirunnu, athu vilamathikkappedaathathikkal valare munbaayirunnu. 1847ll professor sthaanathekku apekshikkaan grassman ithu samarppichappol, mantraalayam ernst commerinode oru report aavasyappettu. athil nalla aashayangalundenn kumar urappu nalkiyengilum, eee vivaranathil kuravundennu kandethukayum, grassman oru sarvakalashaala sthaanam nalkunnathinethire upadeshikkukayum cheythu. adutha 10-oolam varshangalil, thante vipuleekarana sidhaantham prayogichu grassman vaividhyamaarnna kruthikal ezhuthi, athil 1845 leeii "nyoo theori derr electrodynamic", beejaganita vakrangaleyum uparithalangaleyum kurichulla niravadhi prabandhangalum ulppedunnu, eee prayogangal mattullavare thante sidhaanthathe gauravamaayi edukkaan nayikkumenna pratheekshayil.
1846-ll, lebnis aadyamaayi nirddeshicha oru prashnam pariharikkunnathinulla oru malsarathil praveshikkaan mobius grassmennine kshanichu kordinettukalum metrik propertykalum illaatha oru jyaamitheeya calculus aavishkarikkuka (lebnis ithine "analysis sittas" ennu vilikkunnu). graasmanninte "jiometrishe analysis geknupt aan dye voonn lebnis erfunden jiometrishe chaaraktaristik" aayirunnu vijayakaramaya entry (eaka entry). jadjimaaril oraalenna nilayil, aaa ashayangal enthukondaanu moolyavathaayathennathinekku vaayanakkaaran oru avabodhavum nalkaathe grassman amoortha ashayangal avatharippicha reethiye mobius vimarshichu.
1853-ll, nirangal engane kalarunnu ennathinekkurichulla oru sidhaantham grassman prasidheekarichu; addehathinte sidhaanthathinte naalu varnna niyamangal ippozhum graasmaante niyamangalayi padippikkappedunnu. eee vishayathil graasmaante pravartthanangal helmoltsinte pravarthanangalumaayi poruthappedunnilla. christalography, vaidyuthakaanthikatha, mechanics ennivayekkurichum grassman ezhuthi.
1861-ll, grassman thante "leherbuch derr arithmettik" enna kruthiyil peenoyude ganithashaasthrathinte svayamsidhathaykku aditharayittu. 1862-ll, thante vipuleekarana sidhaanthathinu kaalathamasam varuthiya amgeekaaram nedaamennum thante rekheeya beejaganithatthinte krithyamaaya vyaakhyaanam ulkkollumennum pratheekshichukondu grassman eiii 1-nte poornnamaayum thiruthiyezhuthiya randaam pathipp prasidheekarichu. 20-aamm noottaandile paatapusthakangal eiii2 reethi exposion pratheekshikkunnundeng, "kadinamaaya roopathilulla bairbeatettil volstaandig undu" (eiii2) enna phalam eiii1-nekkaal mikachathaayi pravarthichilla.
marupadi.
1840kalil ganithashaasthranjar pothuve graasmaante ashayangal manasilakkaan thayyarayirunnilla. 1860kalilum 1870kalilum vividha ganithashaasthranjar graasmaante aashayangalkk samanamaaya aashayangalilekku vannuvenkilum grassman thanne ganithathil thaalpparyamundaayirunnil.
adhemar jeane claude baare dii seyint-venant 1845ll prasidheekaricha graasmaante samanamaaya oru vekttar calculus vikasippichu. pinneedu randuperil aaraan aadyam aashayangalekkurich chinthichathennu addeham graasmaanumaayi tharkkathil earppettu. 1844ll grassman thante phalangal prasidheekarichirunnavum 1832laanu thaan eee ashayangal aadyamaayi vikasippichathenn vishudha-venant avakashappettu.
thante jeevithakaalathu graasmante aashayangale vilamathicha aadyathe ganithashaasthranjaril oraalaayirunnu herman hankel, addehathinte 1867 leeii "theori derr complexen saahlensistam".
1872-ll victor schlegel thante "sisttam derr romlehre" yude aadya bhagam prasidheekarichu, athu playin jyamithiyil puraathanavum aadhunikavumaaya phalangal labhikkunnathin graasmaante sameepanam upayogichu. shelgalinte pusthakatthinte apoornnathayum pulthakidiyekkurichulla kaazhchappaadukalude abhavavum choondikkaatti felix clain athinekkurichu oru nishedhaathmaka avalokanam ezhuthi. 1875ll schlegel thante "sisttathinte" randaam bhagavumaayi grassmante abhipraayathil pinthudarnnu, ithavana uyarnna alavilulla jyamiti vikasippichu. athesamayam, clain thante erlanchan prograam munnott kondupookukayaayirunnu, ithu jyaamithiyude vyapthiyum vipuleekarichu.
graasmaanekkurichulla dhaarana vekttar speysukal enna aashayathinaayi kaathirunnu, athu addehathinte vipuleekarana sidhaanthathinte multilenear beejaganitam prakadippikkaan kazhiyum. hamiltonecal pulmedukalkku munganana nalkunnathinaayi, veliyettangalekkurichu 1840 leeii lekhanam prasidheekarikkaan josia willard gibbs pulmedukalkku avakaashikalodu abhyarthichu. eiii. enn. whiteheadinte aadyathe monograph, "saarvathrika beejaganitam" (1898), engleeshile vipuleekarana sidhaanthathinteyum baahya beejaganithathinteyum aadyathe chittayaya vyaakhyaanam ulppeduthi. deferential jyaamithiyude uyarchayode baahya beejaganitam deferential roopangalil prayogichu.
1995 ll lloyd sii. cannenberg osdehangsleharinteyum mattu kruthikaludeyum engleesh vivarthanam prasidheekarichu. samakaalika ganithashaasthra bhauthikashaasthrathil graasmaante pravartthanatthinte pankinekkurichulla aamukhathinaayi rogger pentosinte "yaadhaarthyathilekkulla paatha" kaanuka.
bhaashaashaasthranjan.
graasmante ganithashaasthra ashayangal addehathinte jeevithaavasaanathode maathrame vyaapippikkaan thudangiyittulloo. eiii1 prasidheekarichu muppath varshathinu sesham prasadhakan graasmanin ezhuthi "ningalude pusthakam" dye osdehangslehre "kurachukaalamaayi achadichittilla. ningalude srishtikal athra vilppanayillathathinaal, 1864ll ekadesham 600 koppikal maalinya pepparaayi upayogichirunnu, njangalude libraryile oru pakarpp ozhike backie kurachu otta pakarppukal ippol vittupoyi.ganithashaasthra vrithangalil thante pravarthanangalkku labhicha sveekaaryathayil niraasanaaya grassman ganithashaasthranjarumaayulla bandhavum jyaamithiyodulla thaalpparyavum nashtappettu. thante jeevithathinte avasana varshangalil addeham charitraparamaaya bhaashaashaasthrathilekkum samskrithapadanathilekkum thirinju. addeham jarmman vyaakaranathekkurich pusthakangal ezhuthukayum naadodi ganangal shekharikkukayum samskritham padikkukayum cheythu. addeham 2,000 pejulla oru nighanduvum rigvedathinte (1,000 pejiladhikam) vivarthanavum ezhuthi. rigvedam" enna aadhunika padanangalil, graasmaante srishtikal palappozhum udharikkappedunnu. 1955ll addehathinte nighanduvinte moonnaam pathipp puratthirangi.
samskrithathilum greekilum nilanilkkunna oru shabdashaasthra niyamavum grassman shradhikkukayum avatharippikkukayum cheythu. addehathinte bahumaanaartham eee shabdashaasthraparamaaya niyamam grassmans loow ennariyappedunnu.
eee bhaashaashaasthraparamaaya nettangal addehathinte jeevithakaalathu aadarikkappettu. american ooriyantal sosaittiyilekk thiranjedukkappetta addehathinu 1876-ll tubingen sarvakalashaalayil ninnu oonarari doktarettu labhichu.
paraamarshangal.
kurippu vyapakamaaya oonlain grandhasoochika, pullumanushyante jeevithathilum joliyilum samakaalika thaalparyam prakadamaakkunnu. shubringile oro adhyaayatheyum paraamarsikkunnu.

