For vector spaces $V,W$, probe that $\Lambda (V)\otimes\Lambda (W) \cong \Lambda (V\oplus W)$
97800
Exterior power "commutes" with direct sum
110654
Vector Spaces and AC
66283
Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
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 $D?$
89089
Prove that there is a unique inner product on $V$
48524
Existence proof of the tensor product using the Adjoint functor theorem.
83279
How can I find such a $z$? (Injectivity of $T(z) = \lambda z + \mu\bar{z}$)
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$
145104
$T:$ $\mathbb{C}$ $\to$ $\mathbb{C}$ by $T(z)=\lambda z + \mu \bar{z}$ for every $z \in \mathbb{C}$
40094
Does $G\oplus G \cong H\oplus H$ imply $G\cong H$ in general?
73690
If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
35286
number of differents vector space structures over the same field $\mathbb{F}$ on an abelian group
143517
Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
122623
Geometric intuition for the tensor product of vector spaces
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
77969
Question about proof for $S_4 \cong V_4 \rtimes S_3$
6202
$V$ be a vector space , $T:V \to V$ be a linear operator , then is $\ker (T) \cap R(T) \cong R(T)/R(T^2) $?