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Vector Security, Inc. provides commercial and home security systems to about 386,000 customers in North America, including multi-site businesses. [17] The company has services and products consisting of intrusion and fire alarms, video surveillance, mobile and home automation solutions [buzzword], access control, electronic article surveillance, robbery and assault notification, and a range of ...
In particular, the solutions to the differential equation () = form a vector space (over R or C). [ 57 ] The existence of kernels and images is part of the statement that the category of vector spaces (over a fixed field F {\displaystyle F} ) is an abelian category , that is, a corpus of mathematical objects and structure-preserving maps ...
In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract. A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations.
This solution set has the following additional properties: If u and v are two vectors representing solutions to a homogeneous system, then the vector sum u + v is also a solution to the system. If u is a vector representing a solution to a homogeneous system, and r is any scalar, then ru is also a solution to the system.
Vector optimization is a subarea of mathematical optimization where optimization problems with a ... Modern solution concepts not only consists of minimality notions ...
Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form x ˙ = A ( t ) x , {\displaystyle {\dot {x}}=A(t)x,}
Given a unit vector in 3 dimensions, for example (a, b, c), one takes a dot product with the Pauli spin matrices to obtain a spin matrix for spin in the direction of the unit vector. The eigenvectors of that spin matrix are the spinors for spin-1/2 oriented in the direction given by the vector. Example: u = (0.8, -0.6, 0) is a unit vector ...
In mathematics, a fundamental matrix of a system of n homogeneous linear ordinary differential equations ˙ = () is a matrix-valued function () whose columns are linearly independent solutions of the system. [1]