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Minkowski sums act linearly on the perimeter of two-dimensional convex bodies: the perimeter of the sum equals the sum of perimeters. Additionally, if is (the interior of) a curve of constant width, then the Minkowski sum of and of its 180° rotation is a disk.
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 ...
Vector diagram for addition of non-parallel forces. In general, a system of forces acting on a rigid body can always be replaced by one force plus one pure (see previous section) torque. The force is the net force, but to calculate the additional torque, the net force must be assigned the line of action.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
Below, w is stretched by a factor of 2, yielding the sum v + 2w. In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars.
If is a vector subspace of a real or complex vector space then there always exists another vector subspace of , called an algebraic complement of in , such that is the algebraic direct sum of and (which happens if and only if the addition map is a vector space isomorphism). In contrast to algebraic direct sums, the existence of such a ...
The bond valence is a vector directed along the bond since it represents the electrostatic field linking the ions. If the atom is unconstrained, the sum of the bond valence vectors around an atom is expected to be zero, a condition that limits the range of possible bond angles. [10]
In particular, the direct sum of square matrices is a block diagonal matrix. The adjacency matrix of the union of disjoint graphs (or multigraphs) is the direct sum of their adjacency matrices. Any element in the direct sum of two vector spaces of matrices can be represented as a direct sum of two matrices. In general, the direct sum of n ...