Determinants
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In our eReader you can find the full English version of the book. Read Determinants Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Determinants
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. -\-ainAin anA^i-^- . . . +ain^an (tiiAni-h' • '-\-a^nAnn aniAii-\-. . . . -{-annAin «ni^ai+. • •+«nn'^an. • . • an\Ani+. • '+annAi Each element on the principal diagonal of this product is equal to S (Art. I8), while all the other elements vanish (Art. 19). Hence, d. J = S o. . O (J..
, («) == 6", or A o„ o . . . D That is, the reciprocal of a determinant of the «*^ order is equal to its (n — i)*^ power.
Art. 33. Linear Transformations. Let it be required to transform the system ahiXi + ah2X2... + . . . +ahnXn = o [h = i, 2, . . . W] (i) into a new system with the variables Wi, W2j • • • Wn by means of the linear substitutions Xi=biiUi+b2^^2 + ' . . +bniMn' [i=I, 2, . . . W] (2) QUANTICS: INVARIANTS AND COVARIANTS. 45 Making the required transformation, as has been done for the case of two variables in Art. 30, the resulting system is PjlUl +pj2U2 + . . . +pjnUn = 0, [j=I, 2, . . . W] (3) in which pks = cLkibsi + ^^2^52 + . . . + aknbsn- (Eq. 9, Art. 30. ) The determinants of the systems (i), (2), and (3) are thus con- nected by the relation l/'l.
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You can find similar books in the "Read Also" column, or choose other free books by Laenas Gifford Weld to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
. -\-ainAin anA^i-^- . . . +ain^an (tiiAni-h' • '-\-a^nAnn aniAii-\-. . . . -{-annAin «ni^ai+. • •+«nn'^an. • . • an\Ani+. • '+annAi Each element on the principal diagonal of this product is equal to S (Art. I8), while all the other elements vanish (Art. 19). Hence, d. J = S o. . O (J..
, («) == 6", or A o„ o . . . D That is, the reciprocal of a determinant of the «*^ order is equal to its (n — i)*^ power.
Art. 33. Linear Transformations. Let it be required to transform the system ahiXi + ah2X2... + . . . +ahnXn = o [h = i, 2, . . . W] (i) into a new system with the variables Wi, W2j • • • Wn by means of the linear substitutions Xi=biiUi+b2^^2 + ' . . +bniMn' [i=I, 2, . . . W] (2) QUANTICS: INVARIANTS AND COVARIANTS. 45 Making the required transformation, as has been done for the case of two variables in Art. 30, the resulting system is PjlUl +pj2U2 + . . . +pjnUn = 0, [j=I, 2, . . . W] (3) in which pks = cLkibsi + ^^2^52 + . . . + aknbsn- (Eq. 9, Art. 30. ) The determinants of the systems (i), (2), and (3) are thus con- nected by the relation l/'l.
What to read after Determinants?
You can find similar books in the "Read Also" column, or choose other free books by Laenas Gifford Weld to read onlineMoreLess
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