Proof for Dim(V) = Dim(Kernel(T)) + Dim(Image(T)): Is this enough to prove it?
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
76160
Dimension of the sum of two vector subspaces
53364
dim$(V)$ = $n$, dim$(W)$ = $m$ $\implies$ dim($L(V,W)$) = $nm$
7384
How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
359
Show that $\ker \hat{T} = \text{ann}(\text{range } T)$
83815
Identify the universal property of kernels
123505
how to prove vector norm equivalence in finite dimensional space($\mathbb{R}^{n}$)?
102856
Intersection of kernels and linear dependence of functionals
55488
Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
108560
Proof of a Gaussian Integral property
76110
Proving that the zero vector is unique
44281
Proof of sum of kernels of concatenated vector
102371
Proving that two vector spaces of equal dimension are isomorphic
96452
Is the closedness of the image of a Fredholm operator implied by the finiteness of the codimension of its image?
41347
The dimension of the intersection of two vector subspaces
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
124786
Prove that V contains a subspace of each dimension