A
1 Cube word, abbreviated to CW, is expressed by matrix.
2 CW is likened to a house. The first floor is row of matrix and the ground floor is column of it.
3 CW expresses 4 dimensional universe that is developing situation of 3 dimensional universe.
4 Now cube sentence that is the succession of CW, is defined to multiplication of matrix.
5 Cube sentence, abbreviated to CS has non-commutativity by matrix.
6 CS contains uncertainty principle on the basis.
7 CS expresses quantum mechanics.
B
8 Two rooms of a house also express complex plane.
9 The first floor, abbreviated to FF, that is a pair of two rooms, expresses 2 complex planes.
10 FF is expressed by (a+bi)(c+di).
11 FF is also expressed by r(cosα+isinα)s(cosβ+isinβ)=rseiαeiβ=rsei(α+β)
C
12 CW is expressed by matrix. (a1 a2 a3 a4)(b1 b2 b3 b4)
13 When CW is matrix (x y z t) (x y z t), there comes matrix (x2 y2 z2 t2).
14 CW expresses Dirac’s function x2 +y2 +z2 +t2.
15 Dirac’s function is expressed by enlarged CW.
16 Enlarged CW, abbreviated ECW, is the third floor’s house of England
17 Dirac matrix is peculiar one of the house.
18 ECW is also expressed by determinant.
19 Complex of conjugate on square matrix expresses imaginary space.
20 Complex of conjugate also expresses imaginary language that is roughly mentioned in the following papers.
D
21 Imaginary language is connected to Fourier series.
22 Normalized orthogonal basis of ECW is expressed by fn(x)=1/√2πeinx (n=-－∞, ------, +∞).
23 ECW is also connected to infinite dimensional vector space.
24 So ECW is connected to eternally developing language, namely, infinite language.
Hakuba April 1, 2006
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