Proof of linear independence for vectors
107641
Show that an infinite set of families are linearly independent
92600
Let $V$ be a $K$-vector space, $f: V \rightarrow V$ a linear map. Under some condition, show that $v, f(v),...,f^n(v)$ are linearly independent.
31631
Proof Verification: Joint variance of the product of a random matrix with a random vector
44281
Proof of sum of kernels of concatenated vector
76110
Proving that the zero vector is unique
115954
how to find maximal linearly independent subsets
8291
If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
146339
Proof of -(-v)=v in a vector space
94929
Proof that the all bases of a subspace V consist of the same number of vectors?
152495
Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
83449
Proof with 3D vectors
62887
Proof that a linear transformation is continuous
9665
Proof of the independence of the sample mean and sample variance
108742
Proving commutativity of addition for vector spaces
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
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
37794
Proving the two given vectors are orthogonal