Operation algebra: prove [A,f(A)]=0

Thread starter itai
Start date Dec 10, 2010
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Algebra

In summary, the purpose of "Operation algebra: prove [A,f(A)]=0" is to demonstrate the commutativity property of the mathematical operation of algebra. [A,f(A)]=0 represents the commutator of the algebraic operation A and the function f(A), with the result being zero to indicate commutativity. To prove this, one must show that the operation and the function commute, which can be done using mathematical properties. Proving [A,f(A)]=0 is important as it showcases a fundamental concept in mathematics and simplifies equations. This property can be applied to all algebraic operations and functions, with the method of proving varying depending on the specific operation and function.

Dec 10, 2010

itai

Homework Statement

given an opeator A, prove that the commutator satisfies:
[A,f(A)]=0

Homework Equations

[A,f(A)]=Af(A)-f(A)A

The Attempt at a Solution

I don't know how to continue from Af(A)-f(A)A=0
I can't just say that f(A)A=Af(A).
Any ideas?

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Dec 10, 2010

quZz

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1. What is the purpose of "Operation algebra: prove [A,f(A)]=0"?

The purpose of "Operation algebra: prove [A,f(A)]=0" is to demonstrate the commutativity property of the mathematical operation of algebra. This means that the order of operations does not affect the final result.

2. What does [A,f(A)]=0 mean?

The notation [A,f(A)]=0 represents the commutator of the algebraic operation A and the function f(A). The result of this commutator is zero, indicating that the operation and the function commute.

3. How do you prove that [A,f(A)]=0?

To prove that [A,f(A)]=0, you must show that the operation and the function commute, meaning that the order of operations can be interchanged without affecting the final result. This can be done by using mathematical properties and manipulating the equations to show that the commutator is equal to zero.

4. Why is it important to prove [A,f(A)]=0?

Proving [A,f(A)]=0 is important because it demonstrates the commutativity property of algebraic operations, which is a fundamental concept in mathematics. It also helps to simplify equations and make them easier to solve.

5. Can [A,f(A)]=0 be applied to all algebraic operations and functions?

Yes, the commutativity property can be applied to all algebraic operations and functions. However, the specific method of proving the commutator may vary depending on the specific operation and function being used.