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Prepared by State Council of Educational Research and Training (SCERT) Poojappura, Thiruvananthapuram , Kerala Website www scertkeralagov in email scertkerala@gmailcom Phone 0471 , Fax 0471. Recall that if B = {b1,,b n} is a basis for V and v = P x ib i then we write vB for the column vector vB = x1 x n Definition 12 If f is a bilinear form on V and B = {b1,,b n} is a basis for V then we define the matrix of f with respect to B by. Title ViewDocument Author STanikel Created Date 12/21/ AM.

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Proof lnexy = xy = lnex lney = ln(ex ·ey) Since lnx is onetoone, then exy = ex ·ey 1 = e0 = ex(−x) = ex ·e−x ⇒ e−x = 1 ex ex−y = ex(−y) = ex ·e−y = ex · 1 ey ex ey • For r = m ∈ N, emx = e z }m { x···x = z }m { ex ···ex = (ex)m • For r = 1 n, n ∈ N and n 6= 0, ex = e n n x = e 1 nx n ⇒ e n x = (ex) 1 • For r rational, let r = m n, m, n ∈ N. S X A J ` V A x g AT o b N A { 2 B?. 6 2 S e x u a l T ra ffic d Ð i Ð f Ð f Ð e Ð r Ð e Ð n Ð c Ð e Ð s A Jo u rn a l o f F e m in ist C u ltu ra l S tu d ie s 6 2 3 (1 9 9 4 ).

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