Inverse Polynomial in a ring R November 27    1

I just started working on my Bachelor-Thesis in IT-Security and therefore try to understand the NTRUencryption algorithm. It operates on polynomials in a Ring. My problem is that I don't understand how someone computes the inverse of a polynomial in

shortcut for finding a inverse of matrix November 27    3

I need tricks or shortcuts to find the inverse of $2 \times 2$ and $3 \times 3$ matrices. I have to take a time-based exam, in which I have to find the inverse of square matrices.For a 2x2 matrix, the inverse is: $$ \left(\begin{array}{cc} a&b\\ c&

eigenvalue sign of $M\lambda_{k} I$ November 27    1

Let $M$ be a symmetric $n\times n$ tri-diagonal matrix, with positive values in its main diagonal. and let $\mathbf{1} \in R^n$ be the vector of all 1, such $M \mathbf{1} = 0$Suppose $M$ has eigenvalues $0=\lambda_1 < \lambda_2 \leq \cdots \leq \lamb

$\sum _{i=1}^n \sum _{j=1}^n x_i x_j a_{i,j}$ same as quadratic form November 27    1

$\sum _{i=1}^n \sum _{j=1}^n x_i x_j a_{i,j}$ same as quadratic form
I have the quadratic forms equation:I was wondering if the summation would be equal to: $$\sum _{i=1}^n \sum _{j=1}^n x_i x_j a_{i,j}$$Or is there a special reason to represent the sum in th ...

Isomorphism of presheaves November 27    1

I just want you to tell me if a morphism of presheaves $\varphi:\mathscr{F}\to\mathscr{G}$ is an isomorphism iff every map $\varphi_U$ is bijective. I think it is true. Here my proof for the nontrivial implication:Let $V\subseteq U$ and $s\in \mathsc

morphism of constant sheaves November 27

How to show that if $\phi$ is a morphism of sheaves from $K_X$ ro $K_X$, whare $K_X$ is the constant sheaf on $X$, (where $X$ is connected, and locally commected,) then there exista $a$ in $K$ such that $\phi(U)=$'multiplication by a' for all open $U

Vakil's exercise 5.5.# November 27

I'd like to check that my solution to the following exercise of Vakil's FOAG is correct. I am bothered that we have to use (B) in it, and I want to make sure that I used it in the end for the correct reason.5.5.E. EXERCISE (ASSUMING (A) AND (B)). Sho

You Might Also Like