Sufficient conditions for $x, Ax, A^2x, ...$ being linearly indepedent
102529
Prove that the set $\left\{ x, Ax, \dots, A^{k-1} x \right\}$ is linearly independent
126769
Linear independence of columns implies non-zero determinant
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
156910
Necessary and sufficient condition for $R/IJ \cong R/I \times R/J$
145125
How to prove that $A^{-1} + B^{-1}$ is invertible given the conditions
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
156671
Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
50451
The linear dependence of exponential functions
66500
Proving that orthogonal vectors are linearly independent
8291
If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
98298
Prove that bilinear form can be presented as product of linear forms if and only if it has rank one
42495
Determine if the following sets of vectors are linearly independent
150674
Uniqueness in existence of a bilinear form
72920
$x \perp y$ if and only if $\Vert x + \alpha y \Vert \ge \Vert x \Vert$ for all scalars $\alpha$
145447
bilinear form - proof
62237
Characteristic polynomial equals minimal polynomial iff $x, Mx, \ldots, M^{n-1} x$ are linearly independent
3206
Given $ax^2+by^2+cxy > 0$, what can I deduce about $a$, $b$, and $c$?