query: Proving that there exist a nonsingular linear functional for a field of characteristic 0.
positive_passages.docid: 157269
positive_passages.text: If $\alpha_{1},\ldots,\alpha_{m}$ are vectors different from zero vector, then there is a linear functional $f$ such that $f(\alpha_{i})\neq 0$
negative_passages.docid: 101778
negative_passages.text: Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
negative_passages.docid: 89089
negative_passages.text: Prove that there is a unique inner product on $V$
negative_passages.docid: 42332
negative_passages.text: Existence of multiplicative inverse in field $\mathbb{Q}(\sqrt{d})$
negative_passages.docid: 112114
negative_passages.text: Detailed proof that no essential singularity at infinity implies polynomial
negative_passages.docid: 76148
negative_passages.text: Show that $\exists c \in \mathbb{R} : f(c) = 0$
negative_passages.docid: 151018
negative_passages.text: Proving that any finite integral domain is a field.
negative_passages.docid: 73406
negative_passages.text: Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
negative_passages.docid: 119947
negative_passages.text: Can a non-zero vector have zero image under every linear functional?
negative_passages.docid: 12272
negative_passages.text: Why $a$ is not an essential singularity and how $f$ can be extended
negative_passages.docid: 19245
negative_passages.text: Schwartz Distribution Theory: (Non-)Surjectivity of $f \mapsto f*f$ in $ \mathcal E '$
negative_passages.docid: 61539
negative_passages.text: proof for a basis in $L^2$
negative_passages.docid: 128524
negative_passages.text: Proving there is no analytic function
negative_passages.docid: 125723
negative_passages.text: Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
negative_passages.docid: 78143
negative_passages.text: Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
negative_passages.docid: 2717
negative_passages.text: Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
negative_passages.docid: 19153
negative_passages.text: Non-vanishing of Dirichlet $L$ function $L(s,\chi)$ for $Re s=1$