Linked from

The 24 pages that link to Normed vector space, each with the reason it gives.

• Hilbert spaceNarrower topic: Every inner product induces a norm, but not every norm comes from an inner product.

• Metric spaceCompared with: It adds linear structure and a translation-invariant metric absent from general metric spaces.

• Vector spaceBroader topic: A norm adds geometric measurement beyond the vector-space axioms.

• Triangle inequalityNarrower topic: The norm form, ||x + y|| ≤ ||x|| + ||y||, extends the rule to vectors.

• Banach spaceNarrower topic: Banach spaces are precisely the complete members of this broader class.

• Condition numberRelated: Norms make distances and relative perturbations precise for vector-valued problems.

• IsometryRelated: The norm induces a metric, allowing isometries to be studied through vector lengths.

• Euclidean normNarrower topic: The Euclidean norm is one example of the general structure defined by a norm.

• Functional analysisBroader topic: Norms let functional analysis compare functions and define convergence.

• Inner product spaceRelated: Every inner product induces a norm, placing these spaces within normed-space theory.

• Hahn–Banach theoremNarrower topic: The theorem's norm-preserving form applies to functionals on these spaces.

• Riesz representation theoremNarrower topic: Continuity of the functional is defined using the norm on its domain.

• Bounded functionNarrower topic: For vector-valued functions, boundedness is measured with the codomain norm.

• Stefan BanachRelated: Norms provide the structure used in Banach’s central definitions and theorems.

• Fréchet derivativeNarrower topic: Fréchet derivatives compare input and output errors using norms.

• Minkowski inequalityNarrower topic: Minkowski supplies the triangle axiom for the norms defined by p ≥ 1.

• Uniform boundedness principleNarrower topic: The theorem can fail without the completeness required of its Banach-space domain.

• Approximation theoryNarrower topic: Approximation often takes place in spaces where a norm measures the distance between target and approximant.

• Lax–Milgram theoremNarrower topic: Boundedness and coercivity are quantitative statements expressed through norms.

• Schauder fixed-point theoremNarrower topic: Banach spaces are complete normed vector spaces, the theorem’s ambient setting.

• Magnitude (mathematics)Narrower topic: It provides the general setting for defining vector magnitude through a norm.

• Euclidean vectorNarrower topic: Euclidean spaces are normed spaces whose norm comes from an inner product.

• Mazur–Ulam theoremNarrower topic: The theorem applies to normed spaces, without requiring completeness.

• Banach–Mazur theoremNarrower topic: Banach spaces and their isometries are defined using this underlying structure.