Prove that every hyperplane is a null space of a linear functional
91022
How do I prove that a subspace of a vector space $X$ is the null space of some linear functional on $X$?
93160
Null Space of Transformation
86749
Prove that any set of vectors $S \subset \mathbb{R}^n$ containing the zero vector cannot be linearly independent
110669
Linear span of the empty set
116273
Does every $\mathbb{R},\mathbb{C}$ vector space have a norm?
3682
If $V = \text{null}(\textsf{T}-\lambda\textsf{I}) \oplus \text{range}(\textsf{T}-\lambda\textsf{I})$, then prove that $\textsf{T}$ is diagonalizable
67625
$C([0, 1])$ is not complete with respect to the norm $\lVert f\rVert _1 = \int_0^1 \lvert f (x) \rvert \,dx$
26989
Show that C[0,1] is a vector space
90435
Prove that there exist linear functionals $L_1, L_2$ on $X$
125212
How to Show that the Only Subspaces of $R^2$ are the zero subspace, $R^2$ itself, and the lines through the origin
83970
Proof of an elementary property of Projection Operators
108329
If $T\alpha=c\alpha$, then there is a non-zero linear functional $f$ on $V$ such that $T^{t}f=cf$
69766
Is every normed vector space, an inner product space
117575
Every proper subspace of a normed vector space has empty interior
142232
Functional Analysis. Continuous extensions of linear functionals.
141674
Given $n$ linear functionals $f_k(x_1,\dotsc,x_n) = \sum_{j=1}^n (k-j)x_j$, what is the dimension of the subspace they annihilate?
118996
Prove that $T$ is an orthogonal projection