New posts in vector-spaces

For Banach space there is a compact topological space so that the Banach space is isometrically isomorphic with a closed subspace of $C(X)$.

functional-analysis vector-spaces banach-spaces

How can a subspace have a lower dimension than its parent space?

vector-spaces

$W_1^\perp + W_2^\perp = (W_1 \cap W_2 )^\perp$: Can a set be a function? Can two such "functions" be composed?

linear-algebra abstract-algebra vector-spaces orthonormal

Linear Algebra: determine whether the sets span the same subspace

linear-algebra vector-spaces

How to think of a function as a vector?

functions vector-spaces

Complete Lattice, Complemented Lattice, Modular Lattice of Subspaces of a Vector Space

linear-algebra abstract-algebra vector-spaces

Does real dimension equal rational dimension?

linear-algebra vector-spaces

Why don't we study 'metric vector spaces' on their own?

functional-analysis vector-spaces metric-spaces category-theory intuition

Why is one proof for Cauchy-Schwarz inequality easy, but directly it is hard?

real-analysis vector-spaces normed-spaces

Other guises for the vector space $\mathbb{R}^n$?

linear-algebra vector-spaces examples-counterexamples vector-space-isomorphism

Why is an infinite dimensional space so different than a finite dimensional one?

general-topology functional-analysis vector-spaces

Linear Algebra with functions

calculus linear-algebra functional-analysis vector-spaces

Is the uniqueness of the additive neutral element sufficient to prove x+z=x implies z=0?

group-theory proof-verification vector-spaces

Is every vector space basis for $\mathbb{R}$ over the field $\mathbb{Q}$ a nonmeasurable set?

measure-theory vector-spaces axiom-of-choice hamel-basis

how can a set of functions form a vector space?

vector-spaces

Relation between cross-product and outer product

linear-algebra matrices terminology vector-spaces

Does there exist a Hamel basis $\mathcal B$ for $\mathbb R$ over $\mathbb Q$ such that $a,b \in \mathcal B \implies \dfrac ab \in \mathcal B$?

linear-algebra abstract-algebra vector-spaces extension-field

What is the difference between the rowspace and the columnspace in linear algebra?

linear-algebra matrices vector-spaces

$T \in \text{Hom}V $ is nilpotent implies $I - T$ invertible [duplicate]

vector-spaces proof-writing linear-transformations problem-solving nilpotence

How to prove that a seminorm defines a norm?

vector-spaces metric-spaces solution-verification