#### Your Cart

Your cart is empty!

We strive to deliver the best value to our customers and ensure complete satisfaction for all our textbook rentals.

- You can return your online books for any reason within our refund period – no questions asked.
- Every order is available for express shipping, and return shipping is always free.
- You'll be happy with the quality of your books (or we'll ship you another one on our dime).
- You can extend your rental at any time – at the same cheap daily rental rate.
- If you decide to keep the book it will never cost more than the purchase price.

As always, you have access to over 5 million titles. Plus, you can choose from 5 rental periods, so you only pay for what you’ll use. And if you ever run into trouble, our top-notch U.S. based Customer Service team is ready to help by email, chat or phone.

* Free shipping excludes HI, AK and PR.

Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By a proper subset one understands a set included in A, different from the empty set, from the unit element if any, and from A. These types of structures occur in...
Show More

Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By a proper subset one understands a set included in A, different from the empty set, from the unit element if any, and from A. These types of structures occur in our every day's life, that's why we study them in this book. Thus, as a particular case, we investigate the theory of linear algebra and Smarandache linear algebra. A Linear Algebra over a field F is a vector space V with an additional operation called multiplication of vectors which associates with each pair of vectors u, v in V a vector uv in V called product of u and v in such a way that i. multiplication is associative: u(vw) = (uv)w ii. c(uv) = (cu)v = u(cv) for all u, v, w in V and c in F. The Smarandache k-vectorial space of type I is defined to be a k-vectorial space, (A, +, x) such that a proper subset of A is a k-algebra (with respect with the same induced operations and another ‘x’ operation internal on A), where k is a commutative field. The Smarandache vector space of type II is defined to be a module V defined over a Smarandache ring R such that V is a vector space over a proper subset k of R, where k is a field. We observe, that the Smarandache linear algebra can be constructed only using the Smarandache vector space of type II. The Smarandache linear algebra, is defined to be a Smarandache vector space of type II, on which there is an additional operation called product, such that for all a, b in V, ab in V. In this book we analyze the Smarandache linear algebra, and we introduce several other concepts like the Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra. We indicate that Smarandache vector spaces of type II will be used in the study of neutrosophic logic and its applications to Markov chains and Leontief Economic models both of these research topics have intense industrial applications.
Show Less

Out of Stock

So sorry. Try back another time as our inventory fluctuates daily.

Try Another Book?- Normally, new semester rental orders are exactly 125 days.
- With “Bonus Time” you can order early and get a FREE extension until 12/19*.
- It’s our little way of rewarding you early renters for planning ahead.
- But do hurry. The “Bonus Time” offer runs out on 8/8 (11PM PST).

* It can take up to 24 hours for the extension to appear in your account **after you receive** your textbooks.

Since launching the first textbook rental site in 2006, BookRenter has never wavered from our mission to make education more affordable for all students. Every day, we focus on delivering students the best prices, the most flexible options, and the best service on earth. On March 13, 2012 BookRenter.com, Inc. formally changed its name to Rafter, Inc. We are still the same company and the same people, only our corporate name has changed.