Question

Quick question

Answer 1

\[\alpha \beta -\beta \alpha \rightarrow <3\]
the <3 is supposed to be a heart

Answer 2

Prove the previous statement

Answer 3

Are alpha and beta real numbers, vectors, or matrices?

Answer 4

Unknown. Very curious question.

Answer 5

I only need to know in order to use commutative property of multiplication.

Answer 6

I wish I knew. Let's say that it is a matrix of vectors in the imaginary plane.

Answer 7

'Complex plane' you mean, with one real axis and one imaginary axis?

Answer 8

In that case, commutivity of multiplication doesn't necessarily hold. It's indeterminate until I know the vectors contained in those matrices.

(This is fun)

Answer 9

Yes, the complex plane. I do apologize. Imaginary axis was what I meant to say.

Answer 10

By "prove the statement," I have to assume the implication that it is a true statement. That constrains ab-ba to that set of premises which are sufficient for <3 to necessarily follow.

Answer 11

Assuming that the statement is true, what premises is it constrained to?

Answer 12

Unless you mean the arrow of implication merely to point at the next step in the simplification process of an expression and not necessarily a logical argument.

Answer 13

It denotes a logical argument, as you say.

Answer 14

Then the conclusion, <3 is open to interpretation, and could have infinite solutions unless it itself is constrained to a more well-defined system.

Answer 15

For example, if I merely wanted to graph an equation (let's say a polar function) in the complex plane so that the shape of it was a heart, then that's easy enough to do.

Answer 16

Then let's assume that the a is the matrix of all vectors on the complex and real plane with positive value in reference to the horizontal plane, while the b is the matrix of all vectors on both planes with negative values.

Answer 17

All possible*

Answer 18

Also, instead of an arrow, make it an equals sign.

Answer 19

Real plane and complex plane? and horizontal plane? Which one is the horizontal plane? Do you want the solution in three dimensions instead of two?

Answer 20

OK, so it is not an arrow of logical implication, but rather is expressing a statement of equivalence. Ok, fine. Do you have a preference for variables to use, notation, etc?

Answer 21

No, just do it to your whim. Variables are just that, place holders.

Answer 22

Can I get a better definition of the expression on the right-hand side? What are it's qualities, properties, fundamental constraints? Such assumptions will make the process much easier.

Answer 23

Let's assume that the matrix of vectors of a added to the matrix of vectors of b(basically sets of vectors) will provide all the vectors in the known universe. And the right hand side is a constant, which signifies evolution.

Answer 24

Well instead of the known universe, let's say all planes of mathematics, both real and non-real

Answer 25

A constant, which signifies evolution? I'm not sure I understand that. Since evolution is a process of change, signifying it by a constant will lose much of its dynamicism. Are you referring to a constant rate of change such as a derivative?

Answer 26

Hrm... you could say that. The constant for the rate of evolution.

Answer 27

The rate of evolution of what? Biological evolution? Constrained how? Otherwise, it is an ill-formed statement since the rate of biological evolution is not constant (unless you would be satisfied with an average rate of mutations and what not).
And if so, using matrices of vectors (which is a bit redundant since a vector refers to either a row or column of a matrix) in mathematically abstract planes is probably not the best way to go about this.
If it was, I'm sure you would need many more terms than you have provided.