(in continuation )When we say \[A_i=mc_i+nd_i\] are arbitrary it is meant that by applying several values of 'm' and 'n' more than N[in fact far...
Clarification For the fixed set of vectors \[y_i;i=1,2,3....N>>n\] we test the simultaneous validity of \[\Sigma_{i=1}^{i=N}c_iy_i=0\](1) and of...
(in continuation) The subspace W and the subset V-W were considered in deciding on the choice of y_i and of 'e' respectively[as stated earlier(last...
\[e\in V-W \Rightarrow e\in V\] Since \[W\subset V\] we have \[y_i\in W \Rightarrow y_i \in V\] Both e and y_i are elements of V \[\Rightarrow e+y_i...
The topic has been reposted with a brief introduction, with typo corrections on the last post and with additional material in order to induce a...
We consider a linear vector space V of dimension n. W is a proper subspace of V.We take a vector 'e' belonging to V-W and N vectors y_i belonging to...
Four acceleration[1] in terms of coordinate time derivatives in place of proper time derivatives has been considered [ A Wikipedia link has been...
[It might be necessary to refresh the page for viewing the formulas and the equations properly ] For one dimensional motion [along the x axis by way...
We start with the fact that the norm-square of the four acceleration vector is negative or zero. Indeed \[c^2=c^2\left(\frac {dt}{d...
Equation (7) of the last post has been rewritten[it could not be parsed in the last post and there was no time left for editing]:...
Mathematical Theorem If \[\left(a_1^2-a_2^2\right)\left(b_1^2-b_2^2\right)\ge 0\] then either \[\left(a_1b_1-a_2b_2\right)\ge...
In relation to my last post: 1. Keeping alpha beta same , for various selections of gamma and delta R_{alpha beta gamma delta will be the...
Considering the advice of James R[Staff Member]and considering interactions from other forums on this subject: The product of a symmetric and an...
In relation to my last comment that \[R^{\mu\nu}_{\quad\alpha\beta}\] is not formally used, is meant to imply that this tensor or...
QuarkHead: Equation (1) and the facts ensuing from it correct; the only point is that \[R^{\mu\nu}_{\quad \alpha\beta} \] is not formally used....
[It might be necessary to refresh the page for viewing the formulas and the equations] We consider the transformation of the rank two contravariant...
On the Riemann Curvature Tensor Linkhttps://drive.google.com/file/d/1C2-ru6uuDIw9u_e4HQ1bdwa01oKysQ-B/view?usp=sharing Material in Latex[It might be...
In Latex: [One may require to refresh the page for proper viewing] The difference of proper speeds is not a proper speed Indeed...
[One may require to refresh the page for proper viewing] Norm of Four Acceleration Four Acceleration \begin{equation}\left(c\frac{d^2...
[It may be necessary to refresh the page for proper viewing] We start with the norm of proper velocity[metric signature(+,-,-,-)]...
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