query: $V=\mathbb{M}_{n}(\mathbb{F})$, $f\in V^{*}$ with $f(AB)=f(BA),$ exists $\lambda\in\mathbb{F}$ with $f(A)=\lambda\textrm{tr}(A)\,\forall \,A\in V$
positive_passages.docid: 29583
positive_passages.text: Characterization of the trace function
negative_passages.docid: 108329
negative_passages.text: If $T\alpha=c\alpha$, then there is a non-zero linear functional $f$ on $V$ such that $T^{t}f=cf$
negative_passages.docid: 62111
negative_passages.text: Functional Equation $f(mn)=f(m)f(n)$.
negative_passages.docid: 136980
negative_passages.text: Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.
negative_passages.docid: 52711
negative_passages.text: Prove that the sequence $\{v_n\}$ converges to the maximum value of $f$ on $[a,b]$
negative_passages.docid: 152379
negative_passages.text: If $V_1, V_2$ are $\mathbb{Q}$-vector spaces and $f \colon V_1 \to V_2$ is additive, then $f$ is $\mathbb{Q}$-linear
negative_passages.docid: 76148
negative_passages.text: Show that $\exists c \in \mathbb{R} : f(c) = 0$
negative_passages.docid: 157269
negative_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: 155165
negative_passages.text: Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
negative_passages.docid: 68409
negative_passages.text: Consider $f(x,y)=\sup_{θ,φ}\{||e^{i θ }x+ e^{i φ }y||^2: θ,φ∈R\}$ in which $x,y\in\mathbb C^n$
negative_passages.docid: 113892
negative_passages.text: Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
negative_passages.docid: 34712
negative_passages.text: Decomposable elements of $\Lambda^k(V)$
negative_passages.docid: 84871
negative_passages.text: Determining the dimension of span$\{AB-BA : A,B \in M_{n \times n}(\mathbb R) \}$
negative_passages.docid: 83475
negative_passages.text: Prove Or Disprove: tr(AB)=tr(A)*tr(B)
negative_passages.docid: 3682
negative_passages.text: If $V = \text{null}(\textsf{T}-\lambda\textsf{I}) \oplus \text{range}(\textsf{T}-\lambda\textsf{I})$, then prove that $\textsf{T}$ is diagonalizable
negative_passages.docid: 17032
negative_passages.text: If $ab=ba$, Prove $a^2$ commutes with $b^2$
negative_passages.docid: 70512
negative_passages.text: Prove that $\int f\ d\lambda = \int_{a}^{b} f(x)\ dx,$ for any $f \in \mathcal R[a,b].$