Today I can see the matrix that I understand and the understanding of the four-dollar number and the point multiplication and the cross-multiplication.

First, the Matrix and the four-dollar number.

The multiplication of matrices is obtained based on the N*m column, where n is the number of rows representing the result, and the number of columns in M represents the number of columns of the result.

Red and black represent 4 numbers in the first matrix, purple and gray represent the 4 numbers of the second matrix, and the multiplication of the matrix is the result of the first Matrix's N row and the second matrix's M column to multiply and add the flight to the result matrix (n,m) position.

The four-dollar number represents a matrix of [x,y,z,1] * 4*4. Each set of matrices has exactly one value. [1, 0,0,0] [0,1,0,0] [0,0,1,0] [tx,ty,tz,1]. We can actually think of 4 lines of different dimensions. In fact, the matrix is the transformation of the equation expression mode. See Http://www.ruanyifeng.com/blog/2015/09/matrix-multiplication.html for specific understanding

When we represent a rotational angle from a vector of 4-dimensional space, there is no Vientiane-lock deadlock like that of the Euler rotation. The reason is that, with a one-dimensional four element multiplied by a 4*4 matrix, we are able to get a new one-dimensional four-dollar number.

This is why a dimension is added to solve the three-dimensional rotation deadlock. If there is a four-dimensional space, if we want to solve the four-dimensional space deadlock problem I think also need to add a dimension to solve.

From the multiplication of matrices, we speak of the multiplication of points and forks, and the point multiplication is very simple, that is, every element of the two vectors, in accordance with our usual understanding. It's x*x+y*y+z*z, or it can be a b=|a| |. b|cos<a,b> this expression. The result of the point multiplication is that the scalar cannot represent the direction.

Cross-multiplication, such as Wikipedia, https://en.wikipedia.org/wiki/Cross_product the coordinates of each dimension are first multiplied by the unit vectors of XYZ, so the resulting result can describe a vector. (I did not see it too clearly)

While in unity, the angle of rotation is described by the point-multiplication, and the cross-multiplication describes the azimuth, where the understanding of the position is, because the point multiplication is a direction, if the result of the point multiplication is an area, and this face is exactly the direction we need to turn toward the turning point, It is no longer necessary to use the angle to do forward and reverse judgment (if you use the point of view to calculate the direction of the rotation of course, we will appear to be positive or reverse the problem of rotation. And the result of the cross-multiplication is an area, that is, to the sweep of the face, there will only be a direction, the reverse direction of the area and the calculated area asymmetry. This way we omit a point by which the angle is shifted to the left or right.

Thinkings and Tips:

1. There is also a conjecture that the value of x, Y, Z represents a space point. When we're in through another dimension W. To calculate the space point, does not affect the location of x, Y, Z space points. That is how the mathematical principle of the four element is exactly what it looks like.

2. The expression of the matrix can not be understood by the ordinary four-dimensional subtraction, because the matrix is the expression of lines and polygons, and our ordinary operation is only a point. The appearance of matrices is a simplification of the expression of equations. That is, linear mapping.

The difference between matrix and point multiplication and fork multiplication in unity