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Results tagged with inequalities
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user 1306
for questions involving inequalities, upper and lower bounds.
10
votes
An Linear Algebra Inequality
If you replace determinants by traces, then this inequality is just Cauchy-Schwarz for the inner product $(X,Y)=\mathop{\mathrm{tr}}(XY^T)$ on the space of matrices. Now, we just have to recall that d …
- 16.9k
4
votes
Show that $(\sum_{k=1}^{n}x_{k}\cos{k})^2+(\sum_{k=1}^{n}x_{k}\sin{k})^2\le (2+\frac{n}{4})\...
It is a bit long for a comment.
Your question is about the matrix $A=(\cos((i-j)))_{i,j=1\ldots n}$, specifically, the maximum of the quadratic form $q(x)=(Ax,x)$ on the subset $M_+$ of the unit sp …
- 16.9k
3
votes
A property of unimodal sequences
For $k=0$ (a decreasing sequence), the proof is more or less the key idea that makes Leibniz convergence test work, for instance. Since the total alternating sum is zero, you are always reduced to the …
- 16.9k