Dimension is the property of linear space, and the dimension of space refers to the number of vectors contained in its base. Matrix can't form a linear space, let alone a dimension.

In mathematics, there are different views on the dimension of matrix. The dimension of matrix is not defined, and only linear space has dimension.

Broadly speaking, a dimension is the number of abstract concepts that things "connect". "Connected" abstract concept refers to an abstract concept that is connected by multiple abstract concepts, and it is connected with any abstract concept that constitutes it. The number of abstract concepts that make up it is its change dimension, such as area. The basis of this concept is that everything is related.

The number of parameters needed to describe a mathematical object under a certain premise should be completely expressed as "Object X is n dimension based on premise A".

Extended data:

The common understanding is: "A point is 0-dimensional, a straight line is 1 dimensional, a plane is 2-dimensional, and an object is 3-dimensional". In fact, the concept mentioned in this statement is "premise" rather than "described object", and all described objects are "points". Therefore, its complete expression should be "the point based on point is 0 dimension, the point based on line is 1 dimension, the point based on plane is 2 dimension, and the point based on volume is 3 dimension".

Further explanation, the point on the description (positioning) point is the point itself, and no parameters are needed; Describing (locating) a point on a straight line requires 1 parameters (coordinate values); Describing (locating) a point on a plane requires two parameters (coordinate values); Describing (locating) a point on a volume requires three parameters (coordinate values).

If you change the "object", you will get different conclusions, such as: "A straight line is 4-dimensional based on a plane, 6-dimensional based on a straight line, and 9-dimensional based on a plane".

Further explanation, two points can determine a straight line, so describing (locating) a straight line requires 2×2 parameters (coordinate values) on the plane and 2×3 parameters (coordinate values) on the body; A plane can be determined by three points of a line, so 3×3 parameters (coordinate values) are needed to describe (locate) a plane on an object.

Baidu Encyclopedia-Dimension