We measure the large-scale real-space power spectrum Pk using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmologicalparameters from theWilkinson Microwave Anisotropy Probe (WMAP).We employ a matrix-based power spectrum estimation method using Pseudo-Karhunen-Loève eigenmodes, producing uncorrelated minimum-variance measurements in 20 k-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range 0:01h/Mpc <k< 0:2h/Mpc. Results from the LRG and main galaxy samples are consistent, with the former providinghigher signal-to-noise. Our results are robust to omitting angular and radial density fluctuations and areconsistent between different parts of the sky. They provide a striking confirmation of the predicted largescaleΛCDM power spectrum. Combining only SDSS LRG and WMAP data places robust constraints onmany cosmological parameters that complement prior analyses of multiple data sets. The LRGs provideindependent cross-checks on Ωm and the baryon fraction in good agreement with WMAP. Within thecontext of flat ΛCDM models, our LRG measurements complement WMAP by sharpening the constraintson the matter density, the neutrino density and the tensor amplitude by about a factor of 2, giving Ωm = 0:24 ± 0:02 (1σ)), Σmv & 0:9 ≲ eV(95%) and r < 0:3 (95%) and r < 0:3 (95%). Baryon oscillations are clearly detected andprovide a robust measurement of the comoving distance to the median survey redshift z = 0:35independent of curvature and dark energy properties. Within the ΛCDM framework, our power spectrum measurement improves the evidence for spatial flatness, sharpening the curvature constraint Ωtot = 1.05 ± 0.05 from WMAP alone to Ωtot = 1.003 ± 0.010 assuming Ωtot = 1, the equation of stateparameter is constrained to w = -0.94 ± 0.09, indicating the potential for more ambitious future LRGmeasurements to provide precision tests of the nature of dark energy. All these constraints are essentiallyindependent of scales k > 0.1h/Mpc and associated nonlinear complications, yet agree well with moreaggressive published analyses where nonlinear modeling is crucial.