[guest39538]

It would be a start if you learned to spell matrix.
Matrices don't have energy (internal or otherwise) and energy isn't a matrix.

"A ⇒ B means if A is true then B is also true"
OK, that's the conventional use of the symbol, but matrices don't imply anything, not are they implied by anything.
So none of your post makes sense.

Ok lets talk the physics involved in either matrix.


Let us give matrix A dimension and we use a 3*1 matrix

A[uuu]   


Every u in the above matrix is +1e   


The mechanism of the  force in the matrix will cause x to expand?

[u←→u]

[guest39538]

The matrix would be mass-less, without gravity.

A ⇒ B

A+B=G

As maybe Maxwell would put it

→
E(+1e)+E( β−)=G=M

You can't have a mass of something that does not want to stay together......

[Bored chemist]

Let us give matrix A dimension and we use a 3*1 matrix

A[uuu]   


Every u in the above matrix is +1e   

That's not physics.

[guest39538]

Let us give matrix A dimension and we use a 3*1 matrix

A[uuu]   


Every u in the above matrix is +1e   

That's not physics.

Well it certainly is not golf .   You obviously know what I am trying to explain in maths, so why can't you work some of your magic and produce the maths?

Can you read this

If u = <3,-2> and v = <4,5> then u · v = (3)(4) + (-2)(5) = 12 - 10 = 2. (b) If u = 2i + j and v = 5i - 6j then u · v = (2)(5) + (1)(-6) = 10 - 6=4. Proof: We prove only the last property. Let u = <a, b> . Then u · u = <a, b>·<a, b> = a · a + b · b = a2 + b2 = (/a2 + b2)2 except when quantified by any 7point artimace exemplified by stasus elements found in field mortification parameters.
Let u, v and w be three vectors in R3 and let λ be a scalar. (1) v × w = − w × v. (2) u × ( v + w) = u × v + u × w. (3) ( u + v) × w = u × w + v × w. (4) λ( v × w)=(λ v) × w = v × (λ w). We then end up in obvious paradoxity instigated by v x y intigers elevated beyond tartus secondary aspects.

What does it say?

[guest39538]

What is this person saying?

Let's untranslate some of it:

If u = <3,-2> and v = <4,5> then u · v = (3)(4) + (-2)(5) = 12 - 10 = 2.

Looks like the dot product of two vectors, u and v. But, <u,v> (the inner product) is another way to write the dot product
(usually restricted to 2 or 3 dimensional vectors). Hence it should be: If u = (2, -2) and v = (4,5) . . ., otherwise it looks ok.

If u = 2i + j and v = 5i - 6j then u · v = (2)(5) + (1)(-6) = 10 - 6=4.

This uses the i,j,k unit vector notation, looks pretty standard for 2 dimensions.

Let u = <a, b> . Then u · u = <a, b>·<a, b> = a · a + b · b

ok so far, but the rest goes off the rails more than a little.
v × w = − w × v.

Yep. The cross product is antisymmetric. There seems to be no problem with the rest of it, including the scalar multiplication. I have no idea what the "paradoxicity" is. Perhaps it means you shouldn't take any without food or a parachute (or something).

In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative; that is, it satisfies the condition AT = −A.

transpose
transˈpəʊz,trɑːnsˈpəʊz,tranzˈpəʊz,trɑːnzˈpəʊz/Submit
verb
1.
cause (two or more things) to exchange places.
"the situation might have been the same if the parties in opposition and government had been transposed"
synonyms:   interchange, exchange, switch, swap (round), transfer, reverse, invert, rearrange, reorder, turn about/around, change (round), move (around), substitute, trade, alter, convert
"a pair of pictures in which the colours of the flowers and foliage are transposed"
2.
transfer to a different place or context.

[guest39538]

To get that answer I wrote

u ⋅ v=C

u ⇒ v

U[000]+V[000]=U.V


added - I think I am improving?

Let u = <a> and v = <b>. Then u · v = <a>·<b> = a · b

[guest39538]

@Evan  vectors

Is this ok?


evan.jpg (40.92 kB . 1914x922 - viewed 2237 times)

[guest39538]

sorry guys more practise .

[-1,0,0]+[+1,0,0]=[0,0,0]?

Isn't this calculus?

[-1,-1,0]+[+1,+1,0]=[0,0,0]?


[-1,-1,-1]+[+1,+1,+1]=[0,0,0]?

[guest39538]

Δ<[]>  =  Δu = c ~ 1/a

<[]> =empty matrix span

u= internal energy

[guest39538]

raindrops.jpg (22.75 kB . 852x480 - viewed 2297 times)

I sit and watch the rain drops fall onto the flattened state of the pond, the energy of force released in an expanding ripple that fluctuates the calmness of the pond.   
I sit and ask myself a question, where did that raindrop go?   
The pond swallowed it up and the consequence was a tidal wave from where the pond was upset.   

So how do I explain this in matrix form?

[Bored chemist]

I think I am improving

Uniquely.

[Bored chemist]

So how do I explain this in matrix form?

You don't.
Not everything is a matrix.

[guest39538]

So how do I explain this in matrix form?

You don't.
Not everything is a matrix.

Maybe not....   However I could not ''see'' the pond or the rain drop, I could only 'see' the ripple appear then disappear.

[evan_au]

U[000]+V[000]=U.V
 I think I am improving?

Nope.
- The left-hand side is the vector equivalent of addition.
- The right-hand side is (one of) the vector equivalents of multiplication.
- Keep on with the Khan Academy introduction to vectors and matrices (linear algebra).

[-1,0,0]+[+1,0,0]=[0,0,0]?

Much better.
This really is the vector equivalent of addition.

I have no idea why all of a sudden I know about matrices

Vectors and Matrices are a generalisation of the numbers you learned in primary school and high school.
They can do some things that numbers can't do.
But simple numbers can do things that matrices can't, so it's not a perfect generalisation.

For example,
- if a & b are integers, a x b = b x a
- but if A & B are 3x3 matrices, A x B does not necessarily equal B x A.

That gives matrices a lot of power to represent the real world; in the real world, "a rotation around the Z axis followed by a rotation around the X axis" is not the same as "a rotation around the X axis followed by a rotation around the Z axis".

Another example:
- if c is a real number, the inverse of c (c^-1) is defined, providing c is not 0.
- but if C is a 3x3 matrix, the inverse of C (C^-1) is often undefined, even if C is not null.

In the real world, a set of equations may not give a unique answer; you can determine this by solving the equation (which effectively takes the inverse of the matrix).

[guest39538]

U[000]+V[000]=U.V
 I think I am improving?

Nope.
- The left-hand side is the vector equivalent of addition.
- The right-hand side is (one of) the vector equivalents of multiplication.
- Keep on with the Khan Academy introduction to vectors and matrices (linear algebra).

[-1,0,0]+[+1,0,0]=[0,0,0]?

Much better.
This really is the vector equivalent of addition.

I have no idea why all of a sudden I know about matrices

Vectors and Matrices are a generalisation of the numbers you learned in primary school and high school.
They can do some things that numbers can't do.
But simple numbers can do things that matrices can't, so it's not a perfect generalisation.

For example,
- if a & b are integers, a x b = b x a
- but if A & B are 3x3 matrices, A x B does not necessarily equal B x A.

That gives matrices a lot of power to represent the real world; in the real world, "a rotation around the Z axis followed by a rotation around the X axis" is not the same as "a rotation around the X axis followed by a rotation around the Z axis".

Another example:
- if c is a real number, the inverse of c (c^-1) is defined, providing c is not 0.
- but if C is a 3x3 matrix, the inverse of C (C^-1) is often undefined, even if C is not null.

In the real world, a set of equations may not give a unique answer; you can determine this by solving the equation (which effectively takes the inverse of the matrix).

Thank you

I think I finally have my function correct using the eigenvalues and mapping.

How do I describe an isotropic transformation (T) of an empty matrix (a) across an open space K , ?

T(a)=λa/K?

eigenvectors of a?

aX,Y,Z = λX,Y,Z

or

aX,Y,Z=λn?

or mapped

ƒ:a→n?

ƒ:[]→[n]?

n being n-dimension ,   the function in bold being the correct map I think?

[guest39538]

Abstract

ƒ: x=(a→←b) = ƒ:R³=ƒ:xyz=ƒ:(a.b)=ƒ:(a.b)→←(a.b)=ƒ:(a.b)←→(a.b)=Gravity

→
E (A) = negative polarity

→
E (B) = positive polarity

A.B = dot product

(a.b)→←(a.b)

(a.b)←→(a.b)

[Bored chemist]

You seem to be doing to mathematics what this does to the English language.
https://en.wikipedia.org/wiki/Doge_(meme)

[guest39538]

You seem to be doing to mathematics what this does to the English language.
https://en.wikipedia.org/wiki/Doge_(meme)

I should hope so, it is my abstract which attempts to explain gravity mechanism.   It is not my fault it is a different language than you are use to, ostensible things are hard to diagnose so would you really expect the conventional language to be used?

ƒ: x=(a→←b) = ƒ:R³=ƒ:xyz=ƒ:(a.b)=ƒ:(a.b)→←(a.b)=ƒ:(a.b)←→(a.b)=Gravity

Would you like  me to break down the cause and affect that this equation ''illustrates''?

I drew you the first function in the order of events.


function1.jpg (17.8 kB . 882x476 - viewed 2276 times)

[Bored chemist]

so would you really expect the conventional language to be used?

Yes.
Because otherwise nobody will be able to read what you have written.
http://dilbert.com/strip/1992-08-03

[guest39538]

ƒ:R³=ƒ:xyz=ƒ:(a.b)

Read it in pictures, here is function 2 of the order


function2.jpg (22.04 kB . 882x476 - viewed 2239 times)