Tensors waa habab adag oo leh sifooyin gaar ah oo kala duwan. Ururin kasta oo dhinacyo badan leh maaha tensor.

Waxaa jira laba nooc oo tenorso hal-gees ah: Kuwaas waxaa ka mid ah vectors iyo co-vectors. Qaybaha ama vectors-ka midkood waxa loo soo bandhigi karaa sida tirooyin la heli karo.

>Farqiga keliya ayaa ah in isku xidhka labadaas ay timaaddo marka aad haysato lambarro kala duwan oo shayga hal saldhig u ah oo aad rabto in aad ogaato waxa tirooyinka ku adkeynaya isku shay dhul kala duwan.

Calaamadaha is-beddelka iyo xeerarku wax yar ayay ka duwan yihiin fallaadhaha iyo kuwa wada-nooleyaasha. Vectors iyo co-vectors sida caadiga ah waa "tirooyinka tirooyinka" ama "line of tirooyinka", siday u kala horreeyaan. noqo tensor hal-cabbir ah; Haddii aad leedahay tensor hal-cabbir ah, waxa hubaal ah in uu noqon doono vector ama co-vector. Teners-ka laba-geesoodka ah waxaa loo yaqaannaa matrix.

Waxaa jira afar nooc oo kala duwan oo laba-geesood ah, laakiin magacyo gaar ah ma jiraan. Marka laga hadlayo fal-celinta, xeerarka isbeddelku way ka yara duwan yihiin marka aad u guurto mid kale, laakiin ma jiraan magacyo gaar ah oo loogu talagalay kiriyeyaashan: waxay yihiin oo kaliya matrices.

Mar dhow ama ka dib, waxaa lagu magacaabi karaa mid kasta. array laba-cabbir ah "matrix," xitaa haddii aysan ahayn tensor. Mar labaad, faahfaahin dheeraad ah oo ku saabsan faraqa u dhexeeya array iyo tensor, tixraacilaa dooddii hore.

Waxa laga Ogaado Tensors

>>Tensors waa habab adag oo leh hanti gaar ah oo kala duwan.

Tensors waa shay xisaabeed oo loo isticmaali karo in lagu qeexo sifooyin la taaban karo, oo la mid ah qolofyada oo ay la socdaan vectors. Tensors-ku waxay si fudud u yihiin soo-jeedinta scalars iyo vectors; scalar waa 0 darajo tensor, vector-kuna waa tensor darajada 1aad.

Derejada tensor waxaa lagu gartaa tirada jihooyinka (oo markaa cabbirka shaxda) loo baahan yahay si loo qeexo waa. Tusaale ahaan, guryaha u baahan hal hab (ama darajada koowaad) waxaa si fudud loogu sifayn karaa 3×1 vector tiireedka.

Intaa waxaa dheer, guryaha u baahan laba dalab (labaad darajo) waxaa lagu qeexi karaa sagaal lambar, sida ku jirta 3 × 3 matrix guud, 3n coefficients ayaa qeexi kara darajada nth tensor.

Shuruudaha kiraystayaasha darajada labaad waxay timaadaa marka aan u baahanahay inaan ka fikirno wax ka badan hal jiho si aan u qeexno 1 ka mid ah dhinacyadan jireed.

Tusaalaha ugu fiican ee tan waa haddii aan u baahanahay inaan sheegno korantada korantada ee crystal isotropic kasta. Waxaan ognahay in guud ahaan, kirishbooyada isotropic ee u baahan inay adeecaan sharciga Ohm waana; j=σE. Tani waxay ka dhigan tahay in cufnaanta hadda j ay la mid tahay goobta koronto ee go'an, E iyo in qayb kasta oo j ka mid ah ay si toos ah u dhiganto qayb kasta oo E. (tusaale, j1 = σE1).

<10 > 10>

>>QaybahaGoobta Korontada

j1 = σ11E1 + σ12E2 + σ13E3

j2 = σ21E1 + σ22E2 + σ23E3

j3 = σ31E1 + σ32E2 + σ33E3

Qaybaha Korantada

>Si kastaba ha ahaatee, cufnaanta hadda jirta ayaa keentay Maaddada anisotropic lama barbar-dhigi doonto beerta koronto ee ku lug leh sababtoo ah jihooyinka kala duwan ee crystal ee socodka hadda (tusaale fiican oo tani waxay ku jirtaa graphite). Tani waxay soo jeedinaysaa in, guud ahaan, qayb kasta oo ka mid ah vector cufnaanta jira ay ku tiirsanaan karaan dhammaan qaybaha korontada hadda jirta.

Sidaas darteed, guud ahaan, korontadu waa tensor darajada 2aad waxaana lagu hagaajin karaa sagaal coefficients oo madaxbannaan, oo lagu muujin karo matrix 3×3 ah.

Tani waxay ka dhigan tahay in cufnaanta hadda j ay la mid tahay qaybta korontada ee loo qoondeeyey, E iyo in qayb kasta oo j ka mid ah ay si toos ah u siman tahay goob kasta.

16 kiriyeyaasha darajada labaad waxay ka kooban yihiin:>

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• > Nuryeelka korantada
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Waxay guud ahaan ku xidhaan vector-ka faleeg kale ama laba darajo oo kale ilaa scalar. Tensor-yada darajo sare oo dheeraad ah ayaa lagu farayaa inay si buuxda u qeexaan guryaha u sheega laba kirayste oo darajada labaad ah (tusaale, Adag (darajada 4aad): walbahaarka iyo cadaadiska)darajo): walaac iyo kala fogaansho).

Sidoo kale eeg: WEB Rip VS WEB DL: Keebaa Tayada Ugu Wacan? - Dhammaan Farqiga

Si aad u aragto kuwan iyo tusaalooyin kale oo badan oo aad u baarto sida isbeddelka qaybaha tenorsadu u saameeyaan guryahan, u gudub barnaamijka flash-ka ee hoose.

Hordhac tenors

1>

Waa maxay Vector?

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Vector-ku waa 1-cabbir tirooyin ah, jaantus ay m ama n le'eg yihiin 1. Si la mid ah matrixka, waxa suurtogal ah in lagu sameeyo hawlo xisaabeed oo kala duwan vector, wayna fududahay in la sameeyo. Ku dhufo matrijyo leh vectors iyo lidkeeda.

Si kastaba ha ahaatee, tensor-ka waxaa loo malayn karaa inuu yahay matrix guud oo darajadiisu sifayn karto.

Heerka tensor waa lambar wada jir ah 0 ama ka badan. Qalabku wuxuu matali karaa tensor leh darajo 0, tensor leh darajo mid waxaa matali kara vector, matrix-ku wuxuu matali karaa tensor darajada laba. Waxa kale oo jira darajooyin saddex iyo ka sarreeya, kuwa dambe ayaa aad u adag in la qiyaaso.

Marka lagu daro darajada, kiraystayaasha waxay leeyihiin sifooyin gaar ah oo la xiriira sida ay ula falgalaan midba midka kale hay'adaha xisaabta. Haddii mid ka mid ah hay'adaha ku jira is dhexgalka ay beddelaan hay'adda kale ama hay'adaha, markaa kiraystuhu waa inuu adeecaa xeerka isbeddelka ee la midka ah. cabbir cabbirka tirooyinka, oo inta badan loo yaqaan matrix, halkaas oo m ama n = hal.

Dhammaan vectors inta badan waa tenorso. Laakiin dhammaan kiraystayaasha ma noqon karaan faleebo. Tanimacneheedu waa tenors-ku waa shay aad uga baahsan vector-ka (si adag u hadlaya, in kastoo xisaabyahannadu ay ku ururiyaan tenors-yada iyada oo loo marayo vectors). Tensors-ka waxa farsamo ahaan lagu sifeeyaa laba shay oo kala duwan:

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• >Vectors > 20>

Vectors waa shay gaar ah oo aad garanayso waxa tirinaya laba ka mid ah (ku-darka vector) waxay tilmaamaysaa in la miisaami karo (sidoo kale loo yaqaan isku dhufashada scalar).

Sidoo kale eeg: Waa maxay Farqiga u dhexeeya Unugyada Electrolytic iyo Unugyada Galvanic? (Falanqaynta faahfaahsan) - Dhammaan kala duwanaanshaha

Hal foom, sidoo kale, waxay leeyihiin fikrado isku mid ah; Marka laga reebo, waxay ku shaqayn kartaa vectors ka dibna waxay soo celin kartaa scalars. Tusaalooyinka ayaa u kala horreeyaan: Tusaalooyinka ugu caansan waxaa ka mid ah Euclidean vectors - dhibcood oo bannaan.

Tusaaleyaal waxaa ka mid ah hal qaab waxay noqonaysaa magnet-ka "vector" (ma aha "run" vector) ama hawlwadeenka gradient .

Marka aad ku darto mid kale oo habboon malaha, hantida ugu muhiimsan waa in hal-qaab iyo faleefyo u beddelaan si uun iyadoo la beddelayo isku-duwayaasha. Kuwani waa sifooyinka ay dhakhaatiirta fiisigiisku ay inta badan ka walwalaan marka ay la tashadaan waxyaabaha sida aragtida isku xirnaanta guud.

Tensors, by elongation, sida walxaha xisaabtu yihiin hawlwadeeno "multilinear" ah; Tan waxaa la yiraahdaa, waxay qaataan qaybo ka mid ah vectors (iyo hal-qaab) waxayna soo celiyaan tensor kale (oo ka soo horjeeda hawlwadeenada toosan, kuwaas oo qaata vectors iyo soo celinta vectors). Kuwani waxay leeyihiin faa'iidooyin kala duwan.

> ka soo qaadwaxaad rabtaa inaad fahanto aragtida guud ee kiriyeyaasha. Xaaladdaas, waa inaad garataa aljabrada aan la taaban karin iyo aljabrada toosan ee cajiibka ah), iyo haddii aad rabto inaad fahamto xisaabinta tensor, waa inaad sidoo kale fahamtaa aragtida noocyo badan oo kala duwan.

Fikradaha ugu dambeeya

> Maqaalkan, waxaad ku baratay in:>

>Tensors-ku waa habab kala duwan oo leh hanti kala duwan.

Ururin kasta oo dhinacyo badan leh maaha tensor. ama vector ama co-vector. Matrix waa magaca loo bixiyay tenors-ka laba-geesoodka ah.

Vector waa tiro hal-cabbir ah, oo inta badan loo yaqaan matrix, halkaas oo m ama n = 1. A vector, sida matrix, waxaa loo isticmaali karaa in lagu fuliyo hawlo xisaabeed oo kala duwan, wayna fududdahay in lagu dhufto matrijyo leh vectors iyo lidkeeda matrix guud oo lagu sifeeyay darajadiisa -Lafaha, Ribeye, Tomahawk, iyo Filet Mignon)

Farqiga u dhexeeya Cessna 150 iyo Cessna 152 (Isbarbardhigga)