Henning Thielemann wrote:
Let me elaborate on that: In some cases putting vectors as columns into a matrix then applying a matrix operation on this matrix leads to the same like to 'map' a matrix-vector operation to a list of vectors. But in other cases (as the one above) this is not what you want. I consider it as an incidence not as a general principle if this kind of extension works.
Let's consider another example: The basic definition of the Fourier transform is for vectors. MatLab wants to make the effect of vector operations consistent for row and column vectors, thus
Okay, this approach is starting to make sense to me... I can see now that Vectors are a different type of object to Matrices. Vectors represent points in N-Space and matrices represent operations on those points (say rotations or translations)... But it seems we can represent translations as adding vectors or matrix operations (although we need to introduce the 'extra' dimension W... and have an extra field in vectors that contains the value '1'). (3D translation) [x,y,z,1] * [[0,0,0,0],[0,0,0,0],[0,0,0,0],[dx,dy,dz,dw]] = [x+dx,y+dy,z+dz,1+dw] but how is this different from adding vectors? If we allow vector addition then we no longer have the nice separation between values and linear operators, as a value can also be a linear operator (a translation)? Keean.