float matrixA[16] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 };
float matrixB[4][4] = { { 0, 1, 2, 3 }, { 4, 5, 6, 7 }, { 8, 9, 10, 11 }, { 12, 13, 14, 15 } };

matrixA[0] == matrixB[0][0];
matrixA[3] == matrixB[0][3];
matrixA[4] == matrixB[1][0];
matrixA[7] == matrixB[1][3];

1, 0, 0, transX
0, 1, 0, transY
0, 0, 1, transZ
0, 0, 0, 1

x.x x.y x.z 0
y.x y.y y.z 0
z.x z.y z.z 0
p.x p.y p.z 1

{ x.x x.y x.z 0 y.x y.y y.z 0 z.x z.y z.z 0 p.x p.y p.z 1 }

{ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, transX, transY, transZ, 1 }.

mat4 T; vec4 v; vec4 v_transformed;
v_transformed = T*v;

{1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, transX, transY, transZ, 1 }

v_transformed = v*T;

{ 1, 0, 0, transX, 0, 1, 0, transY, 0, 0, 1, transZ, 0, 0, 0, 1 }

mat4 column_matrix = mat4(
    vec4( Xx, Xy, Xz, 0.0),
    vec4( Yx, Xy, Yz, 0.0),
    vec4( Zx  Zy  Zz, 0.0),
    vec4( Tx, Ty, Tz, 1.0) );

vec4 u = column_matrix * v; // multiply the vector from the right to the matrix

mat4 row_matrix = mat4(
    vec4( Xx,  Yx,  Zx,  Tx),
    vec4( Xy,  Yy,  Zy,  Ty),
    vec4( Xz   Yz   Zz,  Tz),
    vec4( 0.0, 0.0, 0.0, 1.0) );

vec4 u = v * row_matrix; // multiply the vector from the left to the matrix

mat2(vec2, vec2);
mat3(vec3, vec3, vec3);
mat4(vec4, vec4, vec4, vec4);

mat2(float, float,
     float, float);

mat3(float, float, float,
     float, float, float,
     float, float, float);

mat4(float, float, float, float,
     float, float, float, float,
     float, float, float, float,
     float, float, float, float);

mat4 matrix=mat4(
     Xx, Xy, Xz, 0.0
     Yx, Xy, Yz, 0.0
     Zx  Zy  Zz, 0.0
     Tx, Ty, Tz, 1.0);

c0  c1  c2  c3
[ Xx  Yx  Zx  Tx ]
[ Xy  Yy  Zy  Ty ]
[ Xz  Yz  Zz  Tz ]
[  0   0   0   1 ]

[ Xx, Xy, Xz, 0,    Yx, Yy, Yz, 0,    Zx, Zy, Zz, 0,    Tx, Ty, Tz, 1 ]

mat2(
    float, float,   // first column
    float, float);  // second column

mat4 m;
m[1] = vec4(2.0); // sets the second column to all 2.0
m[0][0] = 1.0; // sets the upper left element to 1.0
m[2][3] = 2.0; // sets the 4th element of the third column to 2.0

vec3 v, u;
mat3 m;

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]);

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;