# New Classes of Neutrosophic Linear Algebras by W. B. Vasantha Kandasamy

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.

Similar linear books

Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics

This e-book is meant as an introductory textual content just about Lie teams and algebras and their position in a number of fields of arithmetic and physics. it really is written by way of and for researchers who're essentially analysts or physicists, no longer algebraists or geometers. no longer that we have got eschewed the algebraic and geo­ metric advancements.

Dimensional Analysis. Practical Guides in Chemical Engineering

Sensible publications in Chemical Engineering are a cluster of brief texts that every offers a centred introductory view on a unmarried topic. the total library spans the most subject matters within the chemical technique industries that engineering execs require a easy knowing of. they're 'pocket courses' that the pro engineer can simply hold with them or entry electronically whereas operating.

Linear algebra Problem Book

Can one examine linear algebra completely by way of fixing difficulties? Paul Halmos thinks so, and you may too when you learn this e-book. The Linear Algebra challenge e-book is a perfect textual content for a path in linear algebra. It takes the scholar step-by-step from the elemental axioms of a box in the course of the proposal of vector areas, directly to complex thoughts comparable to internal product areas and normality.

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.