Past studies suggested limited dimensionality of the genomic SNP information was related to effective population size (Ne). The objective of this study was to estimate that dimensionality with simulated and with livestock (Holstein, Jersey, Angus, pigs, and chicken) data sets. That dimensionality can be defined as the number of non-negligible singular values of gene content, or the number of non-negligible eigenvalues of genomic relationship matrix (GRM). In this study, eigenvalue analysis determined the numbers of largest eigenvalues corresponding to 90, 95, 98, and 99% of the variation of the GRM for each population. With many genotyped animals and SNP markers, the numbers corresponding to 90, 95, and 98% approached NeL, 2NeL and 4NeL, respectively, where L is genome length in Morgans. Realized accuracies were calculated for single-step GBLUP (ssGBLUP) with an algorithm for inversion of GRM that takes into account the limited dimensionality of the genomic information. Realized accuracies peaked with the dimensionality corresponding to 98 to 99% of variation depending on population, indicating that 1 to 2% of variation in the GRM was due to noise. However, the accuracies were only slightly reduced at half the optimum dimensionality. Subsequently, the dimensionality of the genomic information was estimated at about 14,000 for Holstein and Angus cattle, 12,000 for Jersey cattle, and 6000 for pigs and chickens, which corresponds approximately to 3NeL. Based on interpolation of simulated and real data with L of 30 Morgans, approximate Ne was 149 for Holsteins, 101 for Jerseys, 113 for Angus, and 44 for chickens; for pigs and L of 20 Morgans, approximate Ne was 48. Limited dimensionality of the genomic information has serious implications for genomic prediction and possibly GWAS.