By W. B. Vasantha Kandasamy
During this booklet we introduce 3 forms of neutrosophic linear algebras: neutrosophic set lineat algebra, neutrosophic semigroup linear algebra, and neutrosophic staff linear algebra. those are generalizations of neutrosophic linear algebra. those new algebraic buildings pave the best way for functions in numerous fields like mathematical modeling.
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Additional info for New Classes of Neutrosophic Linear Algebras
Sample text
If W = V then the n-n set linear transformation is defined to be a n-n set linear operator on V. 28: Let °§ m mI 0 · °½ V = ®¨ ¸ m Z ^0`¾ 0¹ ¯°© 0 ¿° and W = {m – mI | m Z+ {0}} be two n-n set linear algebras over the set S = {0, 1, 1 – I} N(Z). Define T: V o W by § m mI 0 · T¨ ¸ = 2m – 2mI 0¹ © 0 for every § m mI 0 · ¨ ¸ V 0¹ © 0 and T(0) = 0. Thus T is a n-n set linear transformation of V into W. 29: Let V = {2ZI} and ½° 0 · °§ 2ZI W = ®¨ ¸ m Z ^0`¾ ¯°© 0 m mI ¹ ¿° be two n-n set linear algebras over the set S = {0, 1, 1 – I} N(Z).
T = {2nI | n Z \ 36 {0}} V is the pure neutrosophic integer set generator of V over S = {0, 1}. 61: Let V = {2I, 9I, –8I, 14I, 27I + 4, 44 – 2I, 0, 14I – 9} PN(Z) be a pure neutrosophic integer set vector space with zero over S = {0,1} Z. , V \ {0} = T is the pure neutrosophic integer set generator of V over S. 62: Let V = {3ZI} be the pure neutrosophic integer set vector space over the set S = Z. T = {3} V is the pure neutrosophic integer set generator of V over S = Z. Thus | T | = 1.
It is important and interesting to note that as in case of linear algebra, n-n linear algebras is a set vector space but in general a n-n set vector space is not a n-n linear algebra. The following examples show that a n-n set vector space is not a n-n set linear algebra. 12: Let V = {3I, 24I, 41I, 26I, 0, –13I, 48I} PN(Z). V is a n-n set vector space over the set S = {0, 1, I} N(Z). We see V is not a n-n set linear algebra over S; as 3I + 24I = 27I V and so on. Thus in general a n-n set vector space is not a n-n set linear algebra over S.