The same solution implies equivalent systems of linear equations
71203
Proving that two systems of linear equations are equivalent if they have the same solutions
114906
For $n \in \mathbb{N}$ and $W \leq \mathbb{F}^n$, there exists a homogeneous system of linear equations whose solution space is $W$
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
51209
A linear transformation satisfying $P^2 = P$
18195
Understanding of the theorem that all norms are equivalent in finite dimensional vector spaces
33591
Product of two matrices sharing the same eigenvector
108885
Systems of equations with a single number
69043
The equivalence relation generated by a relation
138025
How to show the solution of $\dot{x} = Ax $ is an invariant subspace?
62816
Proof that ODE solutions with Wronskian identically zero are linearly dependent
21578
Showing the minimal polynomial for an element in an extension field is the same as the minimal polynomial of a linear transformation.
6091
Similarity of products $AB$ and $BA$ of square matrices
121464
Linearized equations
121765
Semigroups and solutions of equation
106033
Solve the system in $\mathbb{R}$
73297
Two idempotent matrices are similar iff they have the same rank
156827
Prove that the directrix-focus and focus-focus definitions are equivalent