(W,<t,c>); A := H`GroupAlgebra; y1 := H`yxAlgebra.1; y2 := H`yxAlgebra.2; x1 := H`yxAlgebra.3; x2 := H`yxAlgebra.4; //the support of the Cherednik algebra element (as words in the generators) supp := [[ 1 ]]; //the coefficients of the Cherednik algebra ...
So the normal words of F〈X〉 modulo I are those monomials that do not contain a LM (gij) as a factor. Now the theorem follows by Proposition 6.1.1.□ Corollary 6.2.2 The map i: L → U(L) is injective. Proof. By Theorem 6.2.1 the elements x¯i for i≥ 1 are linearly ind...
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Jo started with $315.27 in her bank account. Now that she’s paid for the console, how much can Jo spend on accessories? Let’s start by writing this out in words: We know how much the console costs ($228.95), and we know how much Jo has in her account ($315.27). Now just fil...
For example, the columns of the matrix may be the known words in the vocabulary and rows may be sentences, paragraphs, pages, or documents of text with cells in the matrix marked as the count or frequency of the number of times the word occurred. ...
Scroll through to get a feel for each chapter and what it contains, or use the control-F search function in your browser to look for particular keywords on this page, then jump straight to that section. Realize however that you may need to start reading at the top of the chapter for ...
Part 2. Prove that \left\|AB\right\|\leq \left\|A\right\|\cdot\left\|B\right\| for any operator norm or the Frobenius norm. In other words, any operator norm (or the Frobenius norm) is mutually consistent with itself. Proof. For operator norm, \begin{aligned} \left\|A\right\|...
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And with two vectors in that two dimensional space, it is the area of the parallelogram they form. If the two vectors are parallel to each other (ex: both lie on x-axis). In other words, they are not linearly independent, then the area of the parallelogram between them will become ...