Orthogonal vector group is a set of non-zero pairwise orthogonal (that is, the inner product is 0) vectors.

The concept of geometric vector is abstracted in linear algebra, and a more general concept of vector is obtained. Here, a vector is defined as an element of a vector space. It should be noted that these abstract vectors are not necessarily represented by number pairs, and the concepts of size and direction are not necessarily applicable.

In a three-dimensional vector space, if the inner product of two vectors is zero, the two vectors are said to be orthogonal. Vector analysis of orthogonality first appeared in three-dimensional space. In other words, the orthogonality of two vectors means that they are perpendicular to each other. If the vector α is orthogonal to β, it is recorded as α ⊥ β.

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In mathematics, vectors (also known as Euclidean vectors, geometric vectors and vectors) refer to quantities with magnitude and direction. It can be imagined as a line segment with an arrow. The arrow indicates the direction of the vector; Line segment length: indicates the size of the vector. Only the magnitude corresponds to the vector, and the quantity without direction is called quantity (called scalar in physics).

Vector notation: print letters (such as A, B, U, V) in bold, and add a small arrow "→" at the top of the letter when writing. [1] If the starting point (a) and the ending point (b) of the vector are given, the vector can be marked as AB (plus sign →) at the top. In the spatial cartesian coordinate system, vectors can also be expressed in pairs. For example, (2,3) in the Oxy plane is a vector.

In physics and engineering, geometric vectors are more often called vectors. Many physical quantities are vectors, such as the displacement of an object, the force exerted on it by a ball hitting a wall and so on. On the contrary, it is scalar, that is, a quantity with only size and no direction. Some definitions related to vectors are also closely related to physical concepts. For example, vector potential corresponds to potential energy in physics.

The concept of geometric vector is abstracted in linear algebra, and a more general concept of vector is obtained. Here, a vector is defined as an element of a vector space. It should be noted that these abstract vectors are not necessarily represented by number pairs, and the concepts of size and direction are not necessarily applicable. Therefore, when reading on weekdays, it is necessary to distinguish what kind of concept "vector" is in the text according to the context.

However, we can still find the basis of a vector space to set the coordinate system, and we can also define the norm and inner product on the vector space by choosing a suitable definition, which enables us to compare abstract vectors with specific geometric vectors.

A vector group is a combination of multiple vectors.