Asked by bhj
DEFINED REDUCTION
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Do you mean “define reduction” (i.e., ask for the definition of the term “reduction”)? If so, which context do you want—chemistry, mathematics, computer science/complexity, linear algebra, statistics, or something else?
Below are short, context-specific definitions — tell me which one you want expanded.
- Chemistry: reduction is the gain of electrons by an atom, ion, or molecule (or a decrease in oxidation state). Example: Fe3+ + e− → Fe2+.
- Oxidation–reduction (redox) sense: reduction paired with oxidation; electrons transferred from the oxidized species to the reduced species.
- Mathematics (algebra/fractions): reducing a fraction means rewriting it in lowest terms by dividing numerator and denominator by their greatest common divisor.
- Linear algebra / numerical methods: row reduction (Gaussian elimination) transforms a matrix to row-echelon or reduced row-echelon form to solve linear systems.
- Computer science / algorithms: a reduction is a transformation that converts one problem into another so that a solution to the second yields a solution to the first (e.g., polynomial-time reduction in complexity theory).
- Lambda calculus / term rewriting: beta-reduction is the process of applying a function to an argument by substituting the argument for the function’s parameter.
- Statistics / machine learning: dimensionality reduction is reducing the number of variables under consideration (e.g., PCA).
If you tell me which area you care about, I’ll give a precise definition, properties, and examples.
Below are short, context-specific definitions — tell me which one you want expanded.
- Chemistry: reduction is the gain of electrons by an atom, ion, or molecule (or a decrease in oxidation state). Example: Fe3+ + e− → Fe2+.
- Oxidation–reduction (redox) sense: reduction paired with oxidation; electrons transferred from the oxidized species to the reduced species.
- Mathematics (algebra/fractions): reducing a fraction means rewriting it in lowest terms by dividing numerator and denominator by their greatest common divisor.
- Linear algebra / numerical methods: row reduction (Gaussian elimination) transforms a matrix to row-echelon or reduced row-echelon form to solve linear systems.
- Computer science / algorithms: a reduction is a transformation that converts one problem into another so that a solution to the second yields a solution to the first (e.g., polynomial-time reduction in complexity theory).
- Lambda calculus / term rewriting: beta-reduction is the process of applying a function to an argument by substituting the argument for the function’s parameter.
- Statistics / machine learning: dimensionality reduction is reducing the number of variables under consideration (e.g., PCA).
If you tell me which area you care about, I’ll give a precise definition, properties, and examples.
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