All Questions
4
questions
2
votes
2
answers
783
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Triangle inequality raised to fractional powers [closed]
Does the inequality $|x + y|^\alpha \leq |x|^\alpha + |y|^\alpha$ where $\alpha \in [0, 1)$, hold for all $x,y$ ??
0
votes
1
answer
400
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How can I find the cubic polynomial, using $4\times4$ linear system with coefficients? Or any help of reference?
part A
in standard form $$y = a_0 + a_1t + a_2t^2 + a_3t^3$$ passes points $$(0, 4), (1, 3), (−1, 7), (2, −2)$$
part B
and for the same cubic polynomial in shifted basis
$$\{1, t − 2,(t − 2)^2,(...
- 47
0
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0
answers
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How to calculate the $k$-dimension of a subspace of a polynomial ring? [duplicate]
Let $k$ be an infinite field and $R:=k[x_1,...,x_n]$ the polynomial ring in $n$ indeterminates.
Why is the $k$-dimension of $U$ given by $\begin{pmatrix} n+m-1 \\ m\end{pmatrix}$, when $U$ is the ...
- 540
0
votes
1
answer
88
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expressing canonical base of univariate polynomials in binomial base
Two bases are fairly standard for ${\mathbb Q}[X]$ : the canonical base
$(X^j)_{j\geq 0}$ and the binomial base $(b_j(X))_{j\geq 0}$ where
$b_j(X)=\binom{X}{j}=\frac{X(X-1)\ldots (X-(j-1))}{j!}$ (thus ...
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