Does the zero product property hold in vector spaces?
42334
Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?
91022
How do I prove that a subspace of a vector space $X$ is the null space of some linear functional on $X$?
151117
Are all fields vector spaces?
29030
Vector space with new scalar multiplication defined over finite field still vector space?
88598
Property of $\{0^n, 1^n, \ldots\}$
120407
Is every noninvertible matrix a zero divisor?
74128
Second exterior power of a complex vector space
108742
Proving commutativity of addition for vector spaces
116273
Does every $\mathbb{R},\mathbb{C}$ vector space have a norm?
7813
In a complex vector space, $\langle Tx,x \rangle=0 \implies T = 0$
2762
Mapping of zero vector under a linear transformation
137873
Problems that involves two facts in the definition of vector spaces
153107
Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?
86362
Cyclic vectors in a real vector space
18373
Can infinite-dimensional vector spaces be decomposed into direct sum of its subspaces?
143517
Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
32064
Zero-dimensional matrices