A vector space is a mathematical structure formed by a collection of elements called vectors, which may be added together and multiplied (‘scaled’) by numbers, called scalars in this context. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed below. Texture mapping is a method for adding detail, surface texture, or color to a computer-generated graphic or 3D model. Its application to 3D graphics was pioneered by Dr Edwin Catmull in his Ph.D. thesis of 1974. In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. In electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is an electronic circuit operating on continuous-time analog signals. In computing, hardware acceleration is the use of computer hardware to perform some function faster than is possible in software running on the general-purpose CPU. Examples of hardware acceleration include blitting acceleration functionality in graphics processing units (GPUs) and instructions for complex operations in CPUs. Normally, processors are sequential, and instructions are executed one by one. Various techniques are used to improve performance, hardware acceleration is one of them. In mathematics, a linear **map**, linear mapping, linear transformation, or linear operator (in some contexts also called linear function) is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. As a result, it always **maps** straight lines to straight lines or 0. The expression ‘linear operator’ is commonly used for linear **maps** from a vector space to itself. Image editing encompasses the processes of altering images, whether they be digital photographs, traditional analog photographs, or illustrations. Traditional analog image editing is known as photo retouching, using tools such as an airbrush to modify photographs, or editing illustrations with any traditional art medium. Source.