linmath.h provides the most used types required for programming computer graphics:

• vec3 -- 3 element vector of floats
• vec4 -- 4 element vector of floats (4th component used for homogenous computations)
• mat4x4 -- 4 by 4 elements matrix, computations are done in column major order
• quat -- quaternion

The types are deliberately named like the types in GLSL. In fact they are meant to be used for the client side computations and passing to same typed GLSL uniforms.