linear algebra and smarandache linear algebra - w b vasantha kandasamy

... a linear < /b> algebra.< /b> It is worthwhile to mention that by the very definition of linear < /b> algebra < /b> all linear < /b> algebras are vector spaces and < /b> not conversely. 1.2 Linear < /b> transformations and < /b> linear < /b> ... If W < /b> = W < /b> 1 + … + W < /b> k then dim W < /b> = dim W < /b> 1 + … + dim W < /b> k . In fact if B i is an orde...

Ngày tải lên: 31/03/2014, 15:04

... properties of number systems. We won’t do that, of course, but we will review some of the basic sets of numbers, and < /b> assume the reader is familiar with properties of numbers we have not mentioned ... division by nonzero integers is not always possible if we restrict our numbers to integers. The jump from rational to real numbers cannot be entirely explained by algebra,< /b> al- though...

Ngày tải lên: 31/03/2014, 15:02

... step -and-< /b> description form of the algorithms, but nevertheless wish to offer working codes which could be distributed in machine-readable form. I have chosen to present the algorithms in Borland ... networks, an index of software available can be obtained by sending the message SEND INDEX to the pseudo-user NETLIB at node ANL-MCS on the ARPA network (Dongarra and < /b> Grosse 1987)....

Ngày tải lên: 31/03/2014, 15:02

... symmetric bilinear form if f(v, w)< /b> = f (w,< /b> v). Definition 1.3. A bilinear form f(v, w)< /b> is called a skew-symmetric bilinear form or an antisymmetric bilinear form if f(v, w)< /b> = −f (w,< /b> v). Having a bilinear ... space V . We shall call them «wavy» basis and < /b> «non-wavy» basis (because of tilde sign we use for denoting the vectors of one of them). The non-wavy ba...

Ngày tải lên: 31/03/2014, 15:04

... to be known functions on [a, b] . Because the unknown function y(t) is specified at the boundary points a and < /b> b, problem (1.4.1) is known as a two-point boundary value problem. Such problems abound ... set of numbers as described below. Floating-Point Numbers A t -digit, base-β floating-point number has the form f = ±.d 1 d 2 ···d t × β  with d 1 =0, where the base β, the exponent ,...

Ngày tải lên: 08/04/2014, 12:19

... 0 (2. 5b) A solution to this equation can be found in a systematic and < /b> formal way. However, we will take a short cut by using heuristic reasoning. Equation 2.5ab shows that a linear < /b> combination ... John Wiley & Sons, New York, 1958. [3] Lathi, B. P., Signal ProcessingandLinear Systems, Berkeley-CambridgePress,Carmichael,CA, 1998. c  1999 by CRC Press LLC 2 Ordinary Linea...

Ngày tải lên: 27/01/2014, 03:20

... Synchronization and < /b> Linearity • −min(a, b) = max(−a, b) : e ab a ⊕ b = a ⊕ b ab = e b ⊕ e a ; • −max(a, b) = min(−a, b) : e a ⊕ b = e ab a ⊕ b ab = e a ⊗ e b e a ⊕ e b ; • min(a, min (b, c)) = min(min(a, b) , ... c): a bc b ⊕c a ⊕ bc b ⊕c = abc ab ⊕ac ⊕bc and < /b> the symmetryoftheformula with respect to a, b and < /b> c proves the result; • max(c, min(a, b)...

Ngày tải lên: 19/02/2014, 03:20

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Ngày tải lên: 20/02/2014, 18:20

... Spinor and < /b> Quaternion Algebra < /b> 75 6.1 Spinor Algebra:< /b> Quaternion Algebra < /b> 75 6.2 Vector Algebra < /b> 77 6.3 Clifford Algebra:< /b> Grand Synthesis of Algebra < /b> of Grassmann and < /b> Hamilton and < /b> the Geometric Algebra < /b> ... fact, the largest possible associative division algebra < /b> that integrates all algebraic systems (viz., algebra < /b>...

Ngày tải lên: 05/03/2014, 11:21