The sum of the dimensions of the kernel and image set equals the dimension of the vector space
24072
Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$
87692
Basis and dimension of vector space
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
6466
Image of subgroup and Kernel of homomorphism form subgroups
129759
Must an ideal contain the kernel for its image to be an ideal?
26989
Show that C[0,1] is a vector space
131993
Prove that vector space and dual space have same dimension
44710
Vector space of real vectors over field complex scalars.
52596
A basis for $k(X)$ regarded as a vector space over $k$
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
66500
Proving that orthogonal vectors are linearly independent
119782
Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V.
32420
A complete orthonormal system contained in a dense sub-space.
73286
Show that the set of all symmetric, real matrices is a subspace, determine the dimension
72077
''Linear'' transformations between vector spaces over different fields .
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
44281
Proof of sum of kernels of concatenated vector