Formal Proof for $\textbf{Vect}_k\cong\textbf{Mat}_k$?
53772
What's the explicit categorical relation between a linear transformation and its matrix representation?
4652
Is $V$ a simple $\text{End}_kV$-module?
116823
VERIFYING: Proving an $n \times n$ Matrix Vector Space
116538
Proof of Connected Diagrams
67772
How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
52354
Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
42213
Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
114524
Proof Verification: the orthogonal complement of the column space is the left nullspace
13606
Prove that $K$ is isomorphic to a subfield of the ring of $n\times n$ matrices over $F$.
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
43728
Proof via Group Theory : $\mathrm{lcm}(a,b) \cdot \gcd(a,b) = |ab|$
106370
How do we construct the coslice category $C / \bf{C}$ given $\textbf{C}/C$ and prove that the two are equal?
11698
$M /K \land L /K$ algebraic $\implies ML/K$ algebraic?
126561
Proof of equivalence of algebraic and geometric dot product?
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
17191
How to verify $H\otimes K \cong \bigoplus\limits_{i\in I}H$