Read e-book online Algebre lineaire PDF

By Lipschitz S.

ISBN-10: 2704200017

ISBN-13: 9782704200016

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Define IK : V o I [0, 1] by 59 ­ 1 °[0, ] if a i z 0 IK [0, ai] = ® a i ; °[0,1] if a 0. i ¯ IKV is a set fuzzy interval vector space. 4: Let V be a set interval linear algebra over the set S. A set fuzzy interval linear algebra (or fuzzy set interval linear algebra) (V, KI) or VKI is a map KI: V o I [0, 1] such that KI(a + b) t min(KI(a), KI(b)) for every a, b  V. We will illustrate this situation by some examples. 4: Let ­f ½ V = ®¦ [0,a i ]x i a i  Z ‰ {0}¾ ¯i 0 ¿ be a set interval linear algebra over the set S = {0, 1, 2, 5, 7, 13, 16}.

Let P Ž V be a proper subset of V and is a group interval vector space over G. We define P to be a group interval vector subspace over G. We will illustrate this situation by some examples. 39: Let W °­ ª 0 0º ª 0 0 º ª[0, a1 ] [0, a 2 ] 0 º a i  Z15 °½ ®« ¾ » ,« » ,« 0 [0, a 3 ]»¼ 1 d i d 15¿° ¯° ¬[0, a1 ] 0¼ ¬ 0 [0, a 2 ]¼ ¬ 0 42 be a group interval vector space over the group G = Z15. Let ½° 0º °­ ª 0 P = ®« a i  Z15 ¾ Ž V. » ¯° ¬[0, a1 ] 0 ¼ ¿° P is a group interval vector subspace of V over the group G = Z15.

Let T be a mapping from R to S such that T(cD + E) = cT(D) + T(E) for all c  F and D, E  R, then we define T to be a semigroup interval linear transformation from R to S. If R = S we define T to be a semigroup interval linear operator on R. 25: Let R = {[0, n] | n  Z+ ‰ {0}} and S = {[0, n] / n  Q+ ‰ {0}} be two semigroup interval linear algebras over the semigroup F = Z+ ‰ {0}. The map T: R o S is defined by T([0, n]) = [0, n], n  Z+ ‰ {0} is a semigroup interval linear transformation. 26: Let R = {[n, 5n] | n  Z+ ‰ {0}} and S = {[n, 5n] | n  R+ ‰ {0}} be two semigroup interval linear algebras defined over the semigroup F = Z+ ‰ {0}.

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Algebre lineaire by Lipschitz S.


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