query: How to prove the convexity of $\operatorname{Tr}(WLW^T)$, where $L$ is a Laplacian matrix?
positive_passages.docid: 16463
positive_passages.text: Is the function $\mbox{tr}(XAX')$ convex?
negative_passages.docid: 24585
negative_passages.text: Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
negative_passages.docid: 77493
negative_passages.text: Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
negative_passages.docid: 150727
negative_passages.text: Characterization convex function.
negative_passages.docid: 72659
negative_passages.text: How can we define convexity in one dimension?
negative_passages.docid: 15491
negative_passages.text: Prove that $f:\mathbb R^n\to\mathbb R$ is affine if and only if it is convex and concave
negative_passages.docid: 62958
negative_passages.text: Maximize $\mathrm{tr}(Q^TCQ)$ subject to $Q^TQ=I$
negative_passages.docid: 87186
negative_passages.text: Gradient descent of $f(w)=\frac12w^TAw-b^Tw$ viewed in the space of Eigenvectors of $A$
negative_passages.docid: 11557
negative_passages.text: How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
negative_passages.docid: 128361
negative_passages.text: The kernel and range of the powers of a self-adjoint operator
negative_passages.docid: 147420
negative_passages.text: Equivalent definitions of convexity for $f\in\mathcal C^1(\mathbb R^n)$
negative_passages.docid: 54668
negative_passages.text: Proof for the completeness of eigenfunctions of a self-adjoint operator
negative_passages.docid: 142922
negative_passages.text: How to prove that $e^x$ is convex?
negative_passages.docid: 116851
negative_passages.text: Show that f(x) is convex
negative_passages.docid: 122305
negative_passages.text: Proof of matrix norm property: submultiplicativity
negative_passages.docid: 87494
negative_passages.text: $\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
negative_passages.docid: 52231
negative_passages.text: Prove or disprove {$\sum_{i=1}^n x_i^2 = 1$} is convex