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The resulting vector is sometimes called the resultant vector of a and b. The addition may be represented graphically by placing the tail of the arrow b at the head of the arrow a, and then drawing an arrow from the tail of a to the head of b. The new arrow drawn represents the vector a + b, as illustrated below: [7] The addition of two vectors ...
Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work by Miklós Ajtai [ 1 ] who presented a family of one-way functions based on SIS problem.
In mathematics, given a vector at a point on a curve, that vector can be decomposed uniquely as a sum of two vectors, one tangent to the curve, called the tangential component of the vector, and another one perpendicular to the curve, called the normal component of the vector. Similarly, a vector at a point on a surface can be broken down the ...
Macaulay's resultant is a polynomial in the coefficients of these n homogeneous polynomials that vanishes if and only if the polynomials have a common non-zero solution in an algebraically closed field containing the coefficients, or, equivalently, if the n hyper surfaces defined by the polynomials have a common zero in the n –1 dimensional ...
Figure 1: Parallelogram construction for adding vectors. This construction has the same result as moving F 2 so its tail coincides with the head of F 1, and taking the net force as the vector joining the tail of F 1 to the head of F 2. This procedure can be repeated to add F 3 to the resultant F 1 + F 2, and so forth.
If M is such that LCP(q, M) has a solution for every q, then M is a Q-matrix. If M is such that LCP(q, M) have a unique solution for every q, then M is a P-matrix. Both of these characterizations are sufficient and necessary. [4] The vector w is a slack variable, [5] and so is generally discarded after z is found. As such, the problem can also ...
A common problem in computer graphics is to generate a non-zero vector in ℝ 3 that is orthogonal to a given non-zero vector. There is no single continuous function that can do this for all non-zero vector inputs. This is a corollary of the hairy ball theorem. To see this, consider the given vector as the radius of a sphere and note that ...
In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix, the algorithm will produce a number , which is the greatest (in absolute value) eigenvalue of , and a nonzero vector , which is a corresponding eigenvector of , that is, =.