Definitional Material
Quoted from:
Practical Handbook of Digital Mapping Terms and Concepts.
S. L. Arlinghaus; R. F. Austin; W. C. Arlinghaus, W. D. Drake, J. D. Nystuen

pp. 253-254.

    a mathematical entity showing both distance and direction.  In a mapping context, this word has come to refer to a data structure for processing and displaying graphic data, represented as strings of coordinates given the true position of features and their boundaries.  In contrast to the raster format, in which reference is to pixels or matrix entries, the vector format is capable of stringing together pieces of line, end-to-end, in order to create a curve that appears smoother than does its raster counterpart formed from little squares (current shape of a pixel).  Vector data define complex geometric entities that can be manipulated on the basis of attribut data; they are very  useful in this regard.
     From a theoretical standpoint, the distinction between vector and raster is parallel to the approach in linear algebra that distinguishes between combining (using rules of algebra) vectors directly, or combining (using rules of algebra) matrices that represent these vectors.  Thus, one place to look for theoretical material related to the problem of shifting from vector to raster format is in the literature of modern linear algebra texts that emphasize a transformational approach (rather than the first-half of the twentieth century approach of "matrix algebra").