number of cosine waves in DCT Why is it $N\cdot N$ a sufficient number of cosine waves equal to the size of the image or to a portion of it to describe it (or a portion of it) completely without losing information applying the DCT.

For example, in the JPEG encoding I divide the image into 8x8 blocks and I will have, for each block, a table of exactly 8x8 coefficients: one for each wave. But... why?
N orthogonal basis vectors can completely describe a point in N dimensional space.  Same for N * N orthogonal vectors and N * N samples describing an N*N dimensional space.  

A DCT matrix is constructed from an orthonormal set of basis vectors.