The intensity of an isotropically weighted MR image is proportional to a rotationally invariant measure of bulk diffusion, Trace(D) (where D is the effective diffusion tensor). Such images can be acquired from as few as two diffusion-weighted images (DWIs). Analogously, the intensity of an anisotropically weighted MR image is proportional to a rotationally invariant measure of diffusion anisotropy derived from D, such as the variance of the principal diffusivities of D. By using linear algebra, we show that to produce an anisotropically weighted MR image requires acquiring at least seven DWIs, which is also the minimum number of DWIs sufficient to estimate the entire diffusion tensor, as well as the T2-weighted amplitude image, A(b = 0), in each voxel. A general mathematical framework for constructing isotropically weighted and anisotropically weighted MR images is also provided.