matrix multiplication with vector in glsl

Question

Ref http://webglfundamentals.org/webgl/lessons/webgl-3d-orthographic.html In vector shader there is multiplication of `mat4` and `vec4`. ``` attribute vec4 a_position; uniform mat4 u_matrix; void main() { // Multiply the position by the matrix. gl_Position = u_matrix * a_position; } ``` How is it possible to multiply 4*4 matrix with 1*4 matrix? Shouldn't it be `gl_Position = a_position * u_matrix;` Can anybody explain this?

Accepted Answer

From the GLSL spec 1.017

5.11 Vector and Matrix Operations

With a few exceptions, operations are component-wise. When an operator operates on a vector or matrix, it is operating independently on each component of the vector or matrix, in a component-wise fashion.

...matrix multiplied by vector, vector multiplied by matrix, and matrix multiplied by matrix. These do not operate component-wise, but rather perform the correct linear algebraic multiply. They require the size of the operands match.

```
vec3 v, u;
mat3 m;

u = v * m;
```

is equivalent to

```
u.x = dot(v, m[0]); // m[0] is the left column of m
u.y = dot(v, m[1]); // dot(a,b) is the inner (dot) product of a and b
u.z = dot(v, m[2]);
```

And

```
u = m * v;
```

is equivalent to

```
u.x = m[0].x * v.x + m[1].x * v.y + m[2].x * v.z;
u.y = m[0].y * v.x + m[1].y * v.y + m[2].y * v.z;
u.z = m[0].z * v.x + m[1].z * v.y + m[2].z * v.z;
```

or also

```
u = v.x * m[0] + v.y * m[1] + v.z * m[2];
```

matrix multiplication with vector in glsl

Solution

Problem