Why are $(\,f_1,...,f_n)$ linearly independent if $\|\,f_k-e_k\|_2<\dfrac{1}{\sqrt n}$, where $(e_k)$ is an orthonormal basis?
62065
Prove that $v_1, \dots v_n$ is a basis of V.
27072
If $X_1,X_2$ are independent beta then showing $\sqrt{X_1X_2}$ is beta
62237
Characteristic polynomial equals minimal polynomial iff $x, Mx, \ldots, M^{n-1} x$ are linearly independent
94077
Proof of linear independence of $e^{at}$
48291
Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
29230
Orthogonality of Hermite functions
6319
Finding an orthonormal basis for a matrix
114309
T-invariant linear independence
89186
Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$
30720
If the dot product between two vectors is $0$, are the two linearly independent?
12698
Orthonormal basis for $\mathcal{L}^2([0,1])$
18967
Linear independence of $\sin(x)$ and $\cos(x)$
146664
The union of two linearly independent subsets
111031
Matrix rank and linear independence of functions
99105
Are the functions $\sin^n(x)$ linearly independent?
145039
Algebraic independence over $\overline{\mathbb Q}$ and over $\mathbb Q$
97049
If $v_1,...,v_m$ are linearly independent, then the span $v_1+w,...,v_m+w$ has dimension $\ge m-1$