Simple geometry

Dot geometry can be used to characterize or sense the angle between the two vectors is calculated, and the vector b is projected on a direction vector, having the formula:

    Substantially the same as a · b> 0 direction, the angle between 0 ° to 90 °

     a · b = 0 orthogonal, perpendicular to each other  

     Substantially opposite a · b <0 direction, an angle between 90 ° to 180 ° 

 

 

//矩阵乘法
#include <bits/stdc++.h>
using namespace std;
#define N 100
int a[N][N],b[N][N],c[N][N];
int main()
{
    int m,s,n;
    scanf("%d%d%d",&m,&s,&n);
    for(int i =1;i<=n;i++){
        for(int j =1;j<=s;j++){
            scanf("%d",&a[i][j]);
        }
    }
    for(int i =1;i<=s;i++){
        for(int j =1;j<=n;j++){
            scanf("%d",&b[i][j]);
        }
    }
    for(int i=1;i<=m;i++){
        for(int j =1;j<=n;j++){
            for(int k =1;k<=s;k++){
                c[i][j]+=a[i][k]*b[k][j];
            }
        }
    }
    for(int i =1;i<=m;i++){
        for(int j=1;j<=n;j++){
            printf("%d ",c[i][j]);
        }
        printf("\n");
    }
    return 0;
}
 

 

Determinant N rows and N columns

 

 

 

Cross product of geometric meaning:

In the three-dimensional geometry, vector a and vector b is a vector cross product result, more familiar, it is called the normal vector, the vector perpendicular to the plane of vectors a and b thereof.

In the 3D image learning, the cross product is useful, with the through cross product of two vectors, to generate a third vertical a, b of the normal vector to construct X, Y, Z coordinate system.

In two-dimensional space, there is another cross product is a geometrical meaning: aXb equal to the parallel quadrilateral vector a and vector b constituting the area.