nml::mat3 operator*(nml::mat3 lhs, const nml::mat3& rhs)

Return a mat3 that is the product between two mat3.

The product between two mat3 is calculated this way:

\(\begin{bmatrix} lhs.x.x & lhs.y.x & lhs.z.x \\ lhs.x.y & lhs.y.y & lhs.z.y \\ lhs.x.z & lhs.y.z & lhs.z.z \end{bmatrix} * \begin{bmatrix} rhs.x.x & rhs.y.x & rhs.z.x \\ rhs.x.y & rhs.y.y & rhs.z.y \\ rhs.x.z & rhs.y.z & rhs.z.z \end{bmatrix} =\)

\(\tiny \begin{bmatrix} lhs.x.x * rhs.x.x + lhs.y.x * rhs.x.y + lhs.z.x * rhs.x.z & lhs.x.x * rhs.y.x + lhs.y.x * rhs.y.y + lhs.z.x * rhs.y.z & lhs.x.x * rhs.z.x + lhs.y.x * rhs.z.y + lhs.z.x * rhs.z.z \\ lhs.x.y * rhs.x.x + lhs.y.y * rhs.x.y + lhs.z.y * rhs.x.z & lhs.x.y * rhs.y.x + lhs.y.y * rhs.y.y + lhs.z.y * rhs.y.z & lhs.x.y * rhs.z.x + lhs.y.y * rhs.z.y + lhs.z.y * rhs.z.z \\ lhs.x.z * rhs.x.x + lhs.y.z * rhs.x.y + lhs.z.z * rhs.x.z & lhs.x.z * rhs.y.x + lhs.y.z * rhs.y.y + lhs.z.z * rhs.y.z & lhs.x.z * rhs.z.x + lhs.y.z * rhs.z.y + lhs.z.z * rhs.z.z \end{bmatrix}\)

Example

#include "include/mat3.h"
#include <iostream>

int main() {
        nml::mat3 a(1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 10.0f);
        nml::mat3 b = nml::inverse(a);
        nml::mat3 c = a * b;
        std::cout << nml::to_string(c) << std::endl;

        return 0;
}

Result:

[[1.000000, 0.000000, 0.000000], [0.000000, 1.000000, 0.000000], [0.000000, 0.000000, 1.000000]]