A method for implementing general linear transformations on one dimensional optical field distributions in integrated optics is described. This method uses the Bragg selectivity of volume holograms to replace one dimension of the bulk optical vector matrix multiplier. A means of writing appropriate matrices optically using unguided light is also described. Experimental results are presented which demonstrate the diffraction of guided light by holograms written with unguided beams. © 1988 SPIE.