Orthonormal basisIn mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space is an orthonormal basis, where the relevant inner product is the dot product of vectors. The of the standard basis under a rotation or reflection (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for arises in this fashion.
Gröbner basisIn mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K[x1, ..., xn] over a field K. A Gröbner basis allows many important properties of the ideal and the associated algebraic variety to be deduced easily, such as the dimension and the number of zeros when it is finite.
Open-source licenseOpen-source licenses facilitate free and open-source software (FOSS) development. Intellectual property (IP) laws restrict the modification and sharing of creative works. Free and open-source software licenses use these existing legal structures for the inverse purpose of granting freedoms that promote sharing and collaboration. They grant the recipient the rights to use the software, examine the source code, modify it, and distribute the modifications. These licenses target computer software where source code can be necessary to create modifications.
Plane of rotationIn geometry, a plane of rotation is an abstract object used to describe or visualize rotations in space. The main use for planes of rotation is in describing more complex rotations in four-dimensional space and higher dimensions, where they can be used to break down the rotations into simpler parts. This can be done using geometric algebra, with the planes of rotations associated with simple bivectors in the algebra.
GNU General Public LicenseThe GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the four freedoms to run, study, share, and modify the software. The license was the first copyleft for general use and was originally written by the founder of the Free Software Foundation (FSF), Richard Stallman, for the GNU Project. The license grants the recipients of a computer program the rights of the Free Software Definition.
Real coordinate spaceIn mathematics, the real coordinate space of dimension n, denoted Rn or , is the set of the n-tuples of real numbers, that is the set of all sequences of n real numbers. Special cases are called the real line R1 and the real coordinate plane R2. With component-wise addition and scalar multiplication, it is a real vector space, and its elements are called coordinate vectors. The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension as that of the vector space.
Software testingSoftware testing is the act of examining the artifacts and the behavior of the software under test by validation and verification. Software testing can also provide an objective, independent view of the software to allow the business to appreciate and understand the risks of software implementation. Test techniques include, but are not necessarily limited to: analyzing the product requirements for completeness and correctness in various contexts like industry perspective, business perspective, feasibility and viability of implementation, usability, performance, security, infrastructure considerations, etc.
Real projective spaceIn mathematics, real projective space, denoted \mathbb{RP}^n or \mathbb{P}_n(\R), is the topological space of lines passing through the origin 0 in the real space \R^{n+1}. It is a compact, smooth manifold of dimension n, and is a special case \mathbf{Gr}(1, \R^{n+1}) of a Grassmannian space. As with all projective spaces, RPn is formed by taking the quotient of Rn+1 ∖ under the equivalence relation x ∼ λx for all real numbers λ ≠ 0. For all x in Rn+1 ∖ one can always find a λ such that λx has norm 1.
User interfaceIn the industrial design field of human–computer interaction, a user interface (UI) is the space where interactions between humans and machines occur. The goal of this interaction is to allow effective operation and control of the machine from the human end, while the machine simultaneously feeds back information that aids the operators' decision-making process. Examples of this broad concept of user interfaces include the interactive aspects of computer operating systems, hand tools, heavy machinery operator controls and process controls.
RotationRotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis.
