Are there $A,B, C, D$ vector spaces such that $A \oplus B \cong C \oplus D$, and $A\cong C$, but $B\not\cong D$?
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 $D?$
26110
Canonical isomorphism between $\mathfrak{so}(3)$ and $\mathbb R^3$ with vector cross product
89517
Do four dimensional vectors have a cross product property?
112548
Existence of non-trivial linear functional on any vector space
13880
Example of vector space such that $cv = 0$ where $c \ne 0$ and $v \ne \vec{0}$
145600
Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?
88956
For any three vectors $x,y,z\in\mathbb{R}^d$, we have $ \|y-z\|\cdot\|x\|\leq\|x-y\|\cdot\|z\|+\|z-x\|\cdot\|y\|$
51397
If a field $F$ is such that $\left|F\right|>n-1$ why is $V$ a vector space over $F$ not equal to the union of $n$ proper subspaces of $V$
69766
Is every normed vector space, an inner product space
47015
Vector Space Structures over ($\mathbb{R}$,+)
62303
For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
141843
n-dimensional vector space isomorphic to the n-th product of a field as abelian groups
1799
How many k-dimensional subspaces there are in n-dimensional vector space over $\mathbb F_p$?
15184
$C \otimes A \cong C \otimes B$ does not imply $A \cong B$
117131
Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
62770
Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
18373
Can infinite-dimensional vector spaces be decomposed into direct sum of its subspaces?