Prove a set is still linearly independent when transformed using an injective linear map
112231
Showing that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set
154837
mapping properties of $(1−z)^i$
45792
Rigorous proof that surjectivity implies injectivity for finite sets
69509
Showing a Linear Transformation is invertible
72391
linear dependence proof using subsets
51313
Extension of linearly independent set to a basis in an infinite dimensional vector space
102529
Prove that the set $\left\{ x, Ax, \dots, A^{k-1} x \right\}$ is linearly independent
30017
Orthogonality and linear independence
42495
Determine if the following sets of vectors are linearly independent
51483
Prove: If a linear map, $φ: U→V$ is bijective, then $φ(x)=0$ has only the solution $x=0$.
109228
Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent
126769
Linear independence of columns implies non-zero determinant
48419
Difference between $\mathbb{R}$-linear and $\mathbb{C}$-linear maps
132492
If a linear transformation $T$ has $z^n$ as the minimal polynomial, there is a vector $v$ such that $v, Tv,\dots, T^{n-1}v$ are linearly independent
83046
A linear map, continuous at zero, is bounded
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
65472
From injective map to continuous map