query: Show that $\text{trace}(A)\leq \sqrt{n}\sqrt{\text{trace}(AA^t)}$ where $A$ is in $M_{n}(\mathbb{R}).$
positive_passages.docid: 143608
positive_passages.text: Show the Trace$(B)^{2} \leq$ nTrace$(B^{T}B)$
negative_passages.docid: 102817
negative_passages.text: $A,B\in M_{n}(\mathbb{R})$ so that $A>0, B>0$, prove that $\det (A+B)>\max (\det(A), \det(B))$
negative_passages.docid: 152932
negative_passages.text: Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
negative_passages.docid: 23224
negative_passages.text: $\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
negative_passages.docid: 8554
negative_passages.text: Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$
negative_passages.docid: 121706
negative_passages.text: Show $\text{det}(A)$ is divisible by $2^{n-1}$
negative_passages.docid: 27821
negative_passages.text: A problem on rank of $A$ and $\operatorname{adj}(A)$
negative_passages.docid: 101286
negative_passages.text: How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
negative_passages.docid: 156712
negative_passages.text: Geometrical or Physical significance (interpretation) of the inner-product $\langle A,B \rangle := Trace (AB^t)$ over $M_n(\mathbb R)$
negative_passages.docid: 143869
negative_passages.text: Showing that the norm of the canonical projection $X\to X/M$ is $1$
negative_passages.docid: 257
negative_passages.text: Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
negative_passages.docid: 33903
negative_passages.text: Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
negative_passages.docid: 127047
negative_passages.text: How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
negative_passages.docid: 118996
negative_passages.text: Prove that $T$ is an orthogonal projection
negative_passages.docid: 120010
negative_passages.text: Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
negative_passages.docid: 19804
negative_passages.text: How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
negative_passages.docid: 28565
negative_passages.text: Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$