mathematics - abstract and linear algebra

... R-modules in general is important and complex. However the study of F -modules is short and simple – every vector space is free and every subspace is a summand. The core of classical linear algebra ... a and b are integers, not both zero, and G is the collection of all linear combinations of a and b, then G is a subgroup of Z, and its positive generator is the greatest com...

Ngày tải lên: 27/03/2014, 11:48

... characteristic). F - modules may also be called vector spaces and submodules may be called subspaces. The study of R-modules in general is important and complex. However the study of F -modules is short and ... theorems in linear algebra. It is that, up to isometry, there is only one inner product space for each dimension. 102 Linear Algebra Chapter 5 Theorem Suppose each of...

Ngày tải lên: 17/01/2014, 04:20

... be J-orthogonal if A T JA = J, i.e., A T = JA −1 J −1 and J-skew-symmetric if A T J = −JA, i.e., A T = −JAJ −1 . Prove that the Cayley transformation sends J-orthogonal matrices into J-skew-symmetric ... with main notions of linear algebra: linear space, basis, linear map, the determinant of a matrix. Apart from that, all the essential theorems of the standard course of linear alg...

Ngày tải lên: 17/01/2014, 04:20

... z)   2x + z = 3 and −y −3z/2 = −1/2}. How- ever, this second description is not much of an improvement. It has two equa- tions instead of three, but it still involves some hard-to-understand interaction among ... non-leading variables in an echelon-form linear system are free variables. In the echelon form system derived in the above example, x and y are leading variables and z is f...

Ngày tải lên: 27/03/2014, 11:48

... total output and demands for energy. The total output is units. The demands from the three sectors E,M and S are, according to the table data, and respectively. Further, consumers demand units of energy. ... and be sets. Then the intersection of and is defined to be the set and The union of and is the set or The difference of and is the set and EXAMPLE 1.2.2. Let and Then A...

Ngày tải lên: 31/03/2014, 15:02

... floating-point arithmetic. While there are other models of floating-point arithmetic, the additive form is the most common, and is used in the IEEE binary and radix-free floating-point arithmetic standards. ... BASIC (for a Digital Equip- ment Corporation VAX computer) are presented covering linear estimation, statistical distributions and pseudo-random numbers. Nash and Walker-Sm...

Ngày tải lên: 31/03/2014, 15:02

... 450074 Ufa, Russia Phone: 7-( 3472 )-2 3-6 7-1 8 Fax: 7-( 3472 )-2 3-6 7-7 4 Home: 5 Rabochaya street, 450003 Ufa, Russia Phone: 7-( 917 )-7 5-5 5-7 86 E-mails: R Sharipov@ic.bashedu.ru r-sharipov@mail.ru ra sharipov@lycos.com ra ... 512.64 Sharipov R. A. Course of Linear Algebra and Multidimensional Geom- etry: the textbook / Publ. of Bashkir State University —...

Ngày tải lên: 31/03/2014, 15:04

... A necessary and sufficient condition that T be semi-simple is that the minimal 1 Linear Algebra and Smarandache Linear Algebra W. B. Vasantha Kandasamy Department of Mathematics ... definition of linear algebra all linear algebras are vector spaces and not conversely. 1.2 Linear transformations and linear operations In this section we introduce...

Ngày tải lên: 31/03/2014, 15:04

... the right. Use the down -and- right strategy for now, and later more practical strategies will be discussed. 1.2 Gaussian Elimination and Matrices 7 Finally, substitute z = 1 and y = 2 back into the ... representation, β = 2 (binary rep- resentation) is standard, but for pencil -and- paper examples it’s more convenient to use β =10. The value of t, called the precision, and the expone...

Ngày tải lên: 08/04/2014, 12:19