linear algebra and multidimensional geometry - r sharipov

... 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 sharipov@ hotmail.com URL: http://www.geocities.com /r- sharipov ISBN ... http://www.geocities.com /r- sharipov ISBN 5-7 47 7-0 09 9-5 c  Sharipov R. A., 1996 c  Bashkir State...

Ngày tải lên: 31/03/2014, 15:04

... simple interpretation. E XAMPLE 1.2.3. Let and Compute APPLIED LINEAR ALGEBRA AND MATRIX ANALYSIS Thomas S. Shores Author address: C OPYRIGHT c MAY 2000 ALL RIGHTS RESERVED 12 1. LINEAR SYSTEMS ... stands for a matrix algebra system like MATLAB or Octave. Also, the shorthand “CAS” stands for a computer algebra system like Maple, Mathematica or MathCad. A few of the projects are...

Ngày tải lên: 31/03/2014, 15:02

... of programs in BASIC (for a Digital Equip- ment Corporation VAX computer) are presented covering linear estimation, statistical distributions and pseudo-random numbers. Nash and Walker-Smith ... capability to solve linear equations, linear least squares, matrix inverse and generalised inverse, sym- metric matrix eigenproblem and nonlinear least squares problems. The joke back-...

Ngày tải lên: 31/03/2014, 15:02

... a linear algebra. It is worthwhile to mention that by the very definition of linear algebra all linear algebras are vector spaces and not conversely. 1.2 Linear transformations and linear ... linear operator. 14 If V is a vector space over the field K, a linear operator on V is a linear transformation from V into V. If U and T are linear operators...

Ngày tải lên: 31/03/2014, 15:04

... 7-( 917 )-7 5-5 5-7 86 E-mails: R Sharipov@ ic.bashedu.ru r- sharipov@ mail.ru ra sharipov@ lycos.com ra sharipov@ hotmail.com URL: http://www.geocities.com /r- sharipov ISBN 5-7 47 7-0 12 9-0 c  Sharipov R. A., ... C(∇ X A); where A and B are arbitrary differentiable tensor fields, while X and Y are arbi- trary vector fields and ξ is an arbitrary scalar field. P...

Ngày tải lên: 31/03/2014, 15:55

... strictly upper triangular. Note To obtain a matrix which is strictly lower triangular, reverse the order of the basis. 94 Linear Algebra Chapter 5 Exercise Use the transpose principle to write ... support inner products and are thus geometric as well as algebraic objects. The theories for the real and complex cases are quite similar, and both could have been treated here. However, f...

Ngày tải lên: 17/01/2014, 04:20

... 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 algebra are given here with ... 0 and, therefore, at least one of the determinants in the left-hand side is nonzero.  23. NORMAL MATRICES 107 Corollary. For an orthogonal matrix U there exists a skew-symmetric matrix...

Ngày tải lên: 17/01/2014, 04:20

... defined unless the domain and range are specified. 8 Background Chapter 1 Exercise Show there are natural bijections from (R × R 2 )to (R 2 × R) and from (R 2 × R) toR × R × R . These three sets are disjoint, ... 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....

Ngày tải lên: 27/03/2014, 11:48

... (Elementary row operations) There are three types of elementary row operations that can be performed on matrices: 1. Interchanging two rows: R i ↔ R j interchanges rows i and j. 2. Multiplying a row ... also row–equivalent to A, by performing the inverse row–operations R 1 → 1 2 R 1 , R 2 ↔ R 3 , R 2 → R 2 − 2R 3 on B. It is not difficult to prove that if A and B are row–eq...

Ngày tải lên: 31/03/2014, 15:02