How to prove that any two real finite dimensional vector spaces with the same dimension are isomorphic to one another?
102371
Proving that two vector spaces of equal dimension are isomorphic
81471
Finite dimensional spaces
113261
How to find a vector space V and decompositions $V=A\oplus B = C\oplus D$ with $A$ isomorphic to $C$ but $B$ is not isomorphic to $D?$
152325
Every subspace of the dual of a finite-dimensional vector space is an annihilator
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
151467
An infinite generating set of a finite dimensional vector space contains a basis
18373
Can infinite-dimensional vector spaces be decomposed into direct sum of its subspaces?
141843
n-dimensional vector space isomorphic to the n-th product of a field as abelian groups
108742
Proving commutativity of addition for vector spaces
109643
Prove that every isometry on $\mathbb{R}^2$ is bijective
66283
Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
73790
Are two Hilbert spaces with the same algebraic dimension (their Hamel bases have the same cardinality) isomorphic?
104578
Suppose that $V$ is a vector space, and $W$ is a subspace of $V$. If $V$ is finite dimensional, then prove $W$ too must be finite dimensional.
68526
Polynomials as vector spaces?
154762
Dual space of a finite dimensional normed space
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
132300
Dimensions of vector spaces in an exact sequence