You are currently viewing our boards as a guest which gives you limited access to view most discussions and access our other features. By joining our free community you will have access to post topics, communicate privately with other members (PM), respond to polls, upload content and access many other special features. Registration is fast, simple and absolutely free so please, join our community today!
If you have any problems with the registration process or your account login, please contact contact us.
import of Schwarz inequality -
01-09-2008, 03:35 PM
To exist, a triangle plane geometric figure with sides a, b, and c must satisfy the following inequalities: 1. a+b>c, 2. a+c>b, 3. b+c>a. Any two sides can be equal but their sum cannot be less than the third. When all sides are equal then it is an equilateral triangle representing a plane figure of perfect symmetry. The export of these existence conditions by particular definitions becomes the import of a generalized theorem of abstract finite-dimensional spacetime structures. These have been extended into infinite dimensional and also defined over the field of complex numbers with inner products, for example: Hilbert spacetime structures in quantum mechanics. However, these are inherently one-dimensional. Higher dimensions would require outer product spacetime descriptions. Their abstraction still does not exist in the annuals of mathematics.
A real finite-dimensional vector space on which an inner product is defined is usually called a Euclidean space. On the other hand, if extended over the field of complex numbers, it is called a unitary space. If X represents an n-dimensional Euclidean space over the field of real numbers, R, then a mapping h of R into R is called a real bilinear form described by matrices or linear transformations. When and where used to represent space-time structures for squares of energy, they are singular square Hadamard matrices satisfying Schwarz inequality given by |(x,y)|≤|x|∙|y|, where x and y are Hadamard matrices of arbitrary dimensions.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
Re: import of Schwarz inequality -
01-09-2008, 03:58 PM
Quote:
Originally Posted by AntonioLao
To exist, a triangle plane geometric figure with sides a, b, and c must satisfy the following inequalities: 1. a+b>c, 2. a+c>b, 3. b+c>a. Any two sides can be equal but their sum cannot be less than the third. When all sides are equal then it is an equilateral triangle representing a plane figure of perfect symmetry. The export of these existence conditions by particular definitions becomes the import of a generalized theorem of abstract finite-dimensional spacetime structures. These have been extended into infinite dimensional and also defined over the field of complex numbers with inner products, for example: Hilbert spacetime structures in quantum mechanics. However, these are inherently one-dimensional. Higher dimensions would require outer product spacetime descriptions. Their abstraction still does not exist in the annuals of mathematics.
A real finite-dimensional vector space on which an inner product is defined is usually called a Euclidean space. On the other hand, if extended over the field of complex numbers, it is called a unitary space. If X represents an n-dimensional Euclidean space over the field of real numbers, R, then a mapping h of R into R is called a real bilinear form described by matrices or linear transformations. When and where used to represent space-time structures for squares of energy, they are singular square Hadamard matrices satisfying Schwarz inequality given by |(x,y)|≤|x|∙|y|, where x and y are Hadamard matrices of arbitrary dimensions.
I somehow feel there is a fusion link lurking nearby!
regards michael.
Humilty,coupled with boldness,surprises truth to
reveal herself?
Re: import of Schwarz inequality -
01-09-2008, 03:58 PM
Linear Mode
