X,Y and Z operators of some algebra

In summary, X, Y, and Z operators are mathematical symbols used in algebra to represent specific operations or functions. They are used in solving algebraic equations by manipulating and isolating unknown variables. These operators can also be used in other branches of mathematics, such as calculus and statistics. While they cannot be interchangeable with other symbols, they can be combined to represent multiple operations in one equation.
  • #1
zetafunction
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let be X,Y and Z operators of some algebra so

[tex] [X_i , Y_j]= \epsilon _ijkX_k [/tex] where i,j and k range over X, Y and Z

then i define the change of coordinates

[tex] X= rcos(u) [/tex]

[tex] Y= rsin(u) [/tex]

[tex] Z=Z [/tex]

again r, u and Z are new operators, the problem is , how can i find for example what is the value of [tex] [r, u] [/tex] or [tex] [r,z] [/tex] or [tex] [u,z] [/tex] ??
 
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  • #2


If X, Y, and Z are in "some algebra", then what do "r cos(u)" and "r sin(u)" mean?
 

FAQ: X,Y and Z operators of some algebra

1. What are X, Y, and Z operators in algebra?

X, Y, and Z operators are mathematical symbols used in algebra to represent specific operations or functions. These operators can range from basic arithmetic symbols like addition and multiplication, to more complex operations like differentiation or integration.

2. How are X, Y, and Z operators used in solving algebraic equations?

X, Y, and Z operators are used in algebraic equations to manipulate and solve for unknown variables. By applying these operators to both sides of an equation, we can isolate the variable and solve for its value.

3. Can X, Y, and Z operators be used in other branches of mathematics?

Yes, X, Y, and Z operators can be used in various branches of mathematics, such as calculus, statistics, and linear algebra. These operators may have different meanings and functions in each branch, but they all serve the purpose of representing mathematical operations.

4. Are X, Y, and Z operators interchangeable with other symbols in algebra?

No, X, Y, and Z operators have specific meanings and functions in algebra and cannot be interchanged with other symbols. However, they may be used in conjunction with other symbols to represent more complex operations.

5. Can X, Y, and Z operators be combined to represent multiple operations in one equation?

Yes, X, Y, and Z operators can be combined to represent multiple operations in one equation. This allows for more complex equations to be solved by applying a series of operations to both sides of the equation.

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