What is a vector?
Vectors have two main dimensions: size and direction.
Size: The length of the arrow indicates the size
Direction: The direction pointed by the arrow indicates the direction
3 ways to express vectors
Lowercase English letters for general printing (a,b,cEtc.), handwriting is indicated by adding an arrow (→) to the letters a, b, and c, such as
Vectors can be represented by directed line segments. The length of the directed line segment represents the size of the vector, and the size of the vector, that is, the length of the vector.
In the plane rectangular coordinate system, take two unit vectors in the same direction as the x-axis and y-axis, respectively.i.jAs a set of substrates. a is an arbitrary vector in the plane rectangular coordinate system, and the vector a is set with the coordinate origin O as the starting point P as the end point. From the basic theorem of the plane vector, we know that there is only one pair of real numbers (x, y) such that a = xi + yj, so the pair of real numbers (x, y) is called the coordinates of the vector a, and is written as a = (x, y) . This is the coordinate representation of the vector a. Where (x, y) is the coordinates of point P. The vector a is called the position vector of the point P.
In the space rectangular coordinate system, take 3 unit vectors that are the same as the x-axis, y-axis, and z-axis directions, respectively.i.j.kAs a set of substrates. If it is an arbitrary vector in the coordinate system, the vector a is set with the coordinate origin O as a starting point. According to the basic theorem of space, there is only one set of real numbers (x, y, z), so that a = ix + jy + kz, so the real number pair (x, y, z) is called the coordinate of the vector a, and is written as a = (x, y, z). This is the coordinate representation of the vector a. Where (x, y, z) are the coordinates of point P. The vector a is called the position vector of the point P.
Of course, for multi-dimensional space vectors, it can be obtained by analogy.
Matrix representation of vectors
Relationship of scalar, vector, matrix, tensor
These 4 concepts are constantly rising in dimensionality. It is easier to understand the metaphorical explanation with the concept of point-line polyhedron:
Interested parties can learn more about the following: