A list is a basis if norm of difference with orthonormal basis is bounded by given constant less than unity
62065
Prove that $v_1, \dots v_n$ is a basis of V.
2439
If a linear operator has an adjoint operator, it is bounded
34272
Proving definition of norms induced by vector norms
66084
Prove 1-Norm is a Norm
149997
Convolution operator has norm 1 with respect to $L^2$ norm
150572
Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$
143869
Showing that the norm of the canonical projection $X\to X/M$ is $1$
77036
Normed vector spaces over finite fields
82018
Norm equivalence (Frobenius and infinity)
76140
The supremum norm is submultiplicative
144151
An orthonormal set cannot be a basis in an infinite dimension vector space?
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
62425
Equivalent Definitions of the Operator Norm
37924
Equivalence of norms proof
122305
Proof of matrix norm property: submultiplicativity
14550
Every Hilbert space has an orthonomal basis - using Zorn's Lemma
63608
Cauchy sequence in a normed space