Find a basis of the $k$ vector space $k(x)$
52596
A basis for $k(X)$ regarded as a vector space over $k$
100749
How to find bases for a subspace defined by an equation
38412
Basis for tensor products
93550
How to find the matrix representation of an operator from its action on a basis?
141843
n-dimensional vector space isomorphic to the n-th product of a field as abelian groups
86362
Cyclic vectors in a real vector space
26989
Show that C[0,1] is a vector space
88184
Finding the value of $k$ for parallel/orthogonal planes
133561
show that if $K$ is a field then $K[x]$ is principal
158156
Finding the dual basis for the space of polynomials of degree $\leq$ 2
108742
Proving commutativity of addition for vector spaces
48113
Find a basis for the vector space of symmetric matrices with an order of $n \times n$
15811
Finding a basis for a certain vector space of periodic polynomials
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 $D?$
132300
Dimensions of vector spaces in an exact sequence
154724
Every vector space has a basis
94929
Proof that the all bases of a subspace V consist of the same number of vectors?