Search results
Results from the WOW.Com Content Network
That is, D i in a sense generates the one-parameter group of translations parallel to the x i-axis. These groups commute with each other, and therefore the infinitesimal generators do also; the Lie bracket [D i, D j] = 0. is this property's reflection. In other words, the Lie derivative of one coordinate with respect to another is zero.
The same is true if y < x 3 y < 0. If y < x 3 and y > 0 then each point (x,y) has exactly three distinct tangent lines to γ passing through it. The same is true if y > x 3 and y < 0. If y = x 3 and y ≠ 0 then each point (x,y) has exactly two tangent lines to γ passing through it (this corresponds to the cubic having one ordinary root and ...
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
Switching {X,Y} in a graph. A two-graph is equivalent to a switching class of graphs and also to a (signed) switching class of signed complete graphs.. Switching a set of vertices in a (simple) graph means reversing the adjacencies of each pair of vertices, one in the set and the other not in the set: thus the edge set is changed so that an adjacent pair becomes nonadjacent and a nonadjacent ...
In mathematics, a reflection (also spelled reflexion) [1] is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in the axis
This isometry maps the x-axis to itself; any other line which is parallel to the x-axis gets reflected in the x-axis, so this system of parallel lines is left invariant. The isometry group generated by just a glide reflection is an infinite cyclic group. [1]
In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane containing the origin. The Householder transformation was used in a 1958 paper by Alston Scott Householder. [1]
The graph of an involution (on the real numbers) is symmetric across the line y = x. This is due to the fact that the inverse of any general function will be its reflection over the line y = x. This can be seen by "swapping" x with y. If, in particular, the function is an involution, then its graph is its own reflection.