space
Broadly speaking, we define unified all things, the universe is the universe through time and space. For the entire physical world, the two dimensions of time and space is the most important and essential. If you put aside time dimension, you can describe things through space. Space to accommodate things like real-world people, architecture and so within a certain space.
Mathematical Space
Space concept can be extended to other fields, such as mathematics is the space rendezvous and geometry. The most famous is our daily life is the most contact with Euclidean space, corresponding to the ancient Greek mathematician Euclid Euclidean geometry created. With respect to low-dimensional space is mainly planar and three-dimensional geometrical space, which also defines the distance, angle, and the inner product of a predetermined number of concepts relevant constraints.
If the two-dimensional, three-dimensional generalized to finite n-dimensional, two-dimensional from all meet the definition of an n-dimensional space is limited collectively referred to as Euclidean space. What are the main constraints that define it? Euclidean space are five main constraints: distance satisfy the constraints, linear structure satisfies the constraints, satisfies the constraints norm, the inner product satisfies constraints must be limited dimensions.
Vector space
Vector space is a vector corresponding to the object, after the introduction of the concept of vector, deal with many issues will become more simple and clear.
Intuitively we feel the vector space typically two and three dimensional vector space, i.e. corresponding to a plane coordinate system (x and y axes) and three-dimensional coordinates (x axis, y axis and z-axis). But in fact, in addition to the vector space including two and three dimensions, while generalized to finite n-dimensional vector space. It is important that the vector space is a linear constraint constraint, i.e., capable of addition and multiplication, and the number of commutative, associative law, distributive law, and therefore the vector space is also called linear space.
Vector representation
Refers to an amount of a vector having a magnitude and direction of the arrow may be used to indicate the length of an arrow represents the magnitude of the vector, and the arrow represents the direction of the vector. In physics, the concept of using a vector as equivalent vectors, and the computer uses the field vector representing an array or list. Origin in the following figure (0,0,0) P and the point (2,3,5) is determined with a vector, the vector may be expressed as:
Vector abstract things
Vector mathematically defined is abstract, then what does it do it? From a higher perspective, the vector is an abstract way of thinking about things, but also a very useful tool to convert things to be simple and efficient vector system can solve many problems. We can map things as vectors, they can map the characteristics of things to the vector space.
In fact, for anything or features can be abstracted as a vector. The most important thing is represented as a vector loop model treated once after we will be able to establish something abstract into a vector model down and processed.
matrix
Matrix is a rectangular array of m rows and n columns of elements, with respect to the vector, in fact the object can be seen as a matrix consisting of a set of vectors. For example, in front of the word vector, m is the matrix of a particular row, then if a specified number of n-word number, it is m rows and n columns of the matrix.
For vector space, the nature of the role of the matrix is applied to transform the operation of the vector that is used to describe the transformation matrix. For example the following expression, the vector x after the transformation matrix A becomes a vector as described in y.
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