$$ i = \sqrt {-1} $$. Doesn't look much like a matrix.

An empty matrix doesn't sound like it's a matrix either; even the 0-matrix isn't empty because every element is 0.

Thank you for your reply, I respect your maths knowledge and understand I am not your equal in math. I will reply to the rest later today as it is 5.30 am here and I have not been bed yet. I have quoted the above, an empty matrix has 0 dimensions , every element is 0 in the empty matrix.

The Empty Matrix
An

*empty matrix* has one or more dimensions that are equal to zero. A two-dimensional matrix with both dimensions equal to zero appears in the MATLAB® application as []. The expression A = [] assigns a 0-by-0 empty matrix to A.

https://uk.mathworks.com/help/matlab/math/empty-matrices-scalars-and-vectors.html#f1-86384
I understand I was not using (i ) in context to what you would use in vectors, I am using it to express an imaginary matrix, you know like an imaginary friend. I was expressing that the matrix is a thought experiment and imaginary , i.e i = []

I can change it back to (a) if it helps. a=[]

You seem to just be tossing mathematical and physical concepts around, wondering "is this connected to this, maybe it is if I say so", but you clearly don't actually grasp the concepts even at a fundamental level.

I am not tossing the concepts around at all, they are my abstract versions that do not use values. I explained this already . To me , I understand my concepts very well and if only I could get somebody who is good at maths, i.e like yourself, to put the correct maths to my opinion/notions.

My opinions and notions are based on our information, it is not made up nonsense without any foundation for support.

I understand the paradox.

Why can't you just help me with the maths? Maxwell helped Faraday, Planck helped Einstein, why can't one of you help me?

I believe I have the answer to gravity mechanism, are you as scientists really going to just ignore this because I am not as well educated as you?

And on a final note before I go bed, what ever happened to the creation of new maths anyway?

I believe I have sort of created a language with maths symbols, its irony that only I understand it.

Anyway I will consider what you have wrote in advice and correct information and try to learn it.

In the mean time does anyone know how to transpose a=[] t0 a=[n] in a split second, in maths terms?

What would be the correct function mapping?

After the advice of the post and a little more thought, I will throw out

ƒ:a→a?

Would that be correct?