Tenzory - Operatsii Nad Tenzoramy, Zovnishniy Dobutok, Odynychnyy Antysymetrychnyy Tenzor, Intehraly Gausa, Tenzornyy Dobutok, Bivektor (Ukrainian, Paperback)

Dzherelo: Wikipedia. Storinky: 23. Hlavy: Operatsii nad tenzoramy, Zovnishniy dobutok, Odynychnyy antysymetrychnyy tenzor, Intehraly Gausa, Tenzornyy dobutok, Bivektor, Tenzory Ey nshtey na ta Richchi, Alhebrai chna totozhnist Bianki, Nul ovyy tenzor Rimana, Tenzornyy analiz, Symetrychnyy tenzor vnutrishn oi kryvyny, Notatsiya Ey nshtey na, Z.hortka tenzora, Dyferentsial na totozhnist Bianki, Del ta Kronekera, Mnozhennya dvokhelementnoho tenzora, Diada, Tenzorne chyslennya. Vytyah: Operatsii nad tenzoramy Dlya tenzoriv odnoho i toho zh typu oznachayet sya operatsiya dodavannya. A same, nekhay aj1...jqi1...ir I b j1...jqj1...jp - komponenty dvokh tenzoriv A i V odnakovoho typu (r, q) zh bazysi e1, ..., en. Zistavymo ts omu bazysu (r+q)-vymirnu matrytsyu, elementamy yakoi ye sumy vidpovidnykh komponent tenzoriv A i V: s j1...jqi1...ir = aj1...jqi1...ir + b j1...jqj1...jp .Z, yasuyemo, yak peretvoryuyet sya elementy s j1...jqi1...ir pry perekhodi do novoho bazysu: s j1...jqi1...ir = aj1...jqi1...ir + b j1...jqj1...jp= j1l1... jql1 k1i1... kpip al1...lqk1...kr+ j1l1... jql1 k1i1... kpip b l1...lqk1...kp= j1l1... jql1 k1i1... kpip(aj1...jqi1...ir + b l1...lqk1...kp)= j1l1... jql1 k1i1... kpipc l1...lqk1...kp Otzhe, elementy s j1...jqi1...ir peretvoryuyut sya z.hidno z formuloyu (I), tomu vony ye komponentamy deyakoho tenzora S typu (r, q), YAKYY nazyvayet sya sumoyu tenzoriv A i V: S=A+V. Pry dodavanni tenzoriv i khni vidpovidni komponenty dodayut sya. Takym chynom, operatsii dodavanym vektoriv, liniy nykh ta bilini y nykh funktsiy, liniy nykh operatori zbihayut sya z operatsiyamy dodavannya i kh yak tenzoriv. Oskil ky komponenty tenzoriv ye elementamy deyakoho polya R, to i oznachennya operatsii dodavannya tenzoriv vyplyvaye, shcho tsya operatsiy komutatyvna i asotsiatyvna. Takozh dlya kozhnoho typu (r, q) isnuye takyy tenzor O (vin nazyvayet sya nul ovym tenzorom i y oho komponenty v us i bazysakh rivni nulyu), shcho A+0=A, de A - dovil nyy tenzor takoho samoho typu, i isnuye takyy tenzor -A (vin nazyv...