What does "The corollary of this is that ..." mean?
In such context:

We now come to the geometric interpretation of 3D rotations. We can think about the rows of the matrix as being unit vectors of a new coordinate frame. So, we can think of this as being the u vector, the v vector, the w vector, where x_u is the X coordinate of the u vector, y_u is the Y coordinate of the u vector, and z_u is the Z coordinate of the u vector. Similarly for the v vector and the w vector. When I say the u vector is the axis of the new coordinate frame, the vector u will be equal to x_u times the X direction plus y_u times the Y direction, plus z_u times the Z direction.

The corollary of this is that given 3 orthonormal vectors, and orthonormality means that, this u vector dot with v vector has to be equal to 0, u vector dot with w vector has to be equal 0, v dot w has to be equal to 0, and u, v and w are unit vectors.

Thanks.

Question

What does "The corollary of this is that ..." mean?
In such context:

We now come to the geometric interpretation of 3D rotations. We can think about the rows of the matrix as being unit vectors of a new coordinate frame. So, we can think of this as being the u vector, the v vector, the w vector, where x_u is the X coordinate of the u vector, y_u is the Y coordinate of the u vector, and z_u is the Z coordinate of the u vector. Similarly for the v vector and the w vector. When I say the u vector is the axis of the new coordinate frame, the vector u will be equal to x_u times the X direction plus y_u times the Y direction, plus z_u times the Z direction.

The corollary of this is that given 3 orthonormal vectors, and orthonormality means that, this u vector dot with v vector has to be equal to 0, u vector dot with w vector has to be equal 0, v dot w has to be equal to 0, and u, v and w are unit vectors.

Thanks.

Answer

A corollary is a consequence, something that follows from the things already given or proven.
The English here is imperfect

The corollary of this is that  X and orthonormality means 
"means here is wrong but understandable.

In this case the corollary of the matrix multiple representation of the 3D rotation insight  seems to be that the u,v & w form an orthonormal basis, that is another set of orthogonal & unit norm axes, just as x,y,z do.
.
Saying it is a corollary means that this new fact is derivable from the previous facts.

Answer

trying to speak about vector-algebra in English is awful!  A corollary is a new true proposition that may be inferred from a given proven proposition.

Don’t miss out on the opportunity to learn a language from the comfort of your own home. Browse our selection of experienced language tutors and enroll in your first lesson now!