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Vector Space
Undergraduate
Definition
A set with vector addition and scalar multiplication satisfying specific axioms.
Formulas
\vecu + \vecv ∈ V
Closed under addition
c\vecv ∈ V
Closed under scalar multiplication
Examples
Example 1
Verify that ℝⁿ is a vector space.
Applications
Functional Analysis
Function spaces
Quantum Mechanics
Hilbert spaces
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