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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.
Let us give matrix A dimension and we use a 3*1 matrix A[uuu] Every u in the above matrix is +1e
Quote from: Thebox on 04/02/2018 15:11:58Let 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.
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.
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 · bok 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.
transposetransˈpəʊz,trɑːnsˈpəʊz,tranzˈpəʊz,trɑːnzˈpəʊz/Submitverb1.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.
I think I am improving
So how do I explain this in matrix form?
Quote from: Thebox on 05/02/2018 15:25:20So how do I explain this in matrix form? You don't.Not everything is a matrix.
U[000]+V[000]=U.V I think I am improving?
[-1,0,0]+[+1,0,0]=[0,0,0]?
I have no idea why all of a sudden I know about matrices
Quote from: TheBoxU[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).Quote[-1,0,0]+[+1,0,0]=[0,0,0]? Much better.This really is the vector equivalent of addition.QuoteI have no idea why all of a sudden I know about matricesVectors 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).
You seem to be doing to mathematics what this does to the English language.https://en.wikipedia.org/wiki/Doge_(meme)
so would you really expect the conventional language to be used?
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