We present the radial velocities , metallicities and the K-band magnitudes of 74 RR Lyrae stars in the inner regions of the LMC .
The intermediate resolution spectra and infrared images were obtained with FORS1 at the ESO VLT and with the SOFI infrared imager at the ESO NTT .
The best 43 RR Lyrae with measured velocities yield an observed velocity dispersion of \sigma = 61 \pm 7 km s ^ { -1 } .
We obtain a true LMC RR Lyrae velocity dispersion of \sigma = 53 km s ^ { -1 } , which is higher than the velocity dispersion of any other LMC population previously measured .
This is the first empirical evidence for a kinematically hot , metal-poor halo in the LMC as discussed in Minniti et al .
( 2003 ) .
Using Layden ’ s ( 1994 ) modification of the \Delta S method we measured the metallicity for 23 of our stars .
The mean value is [ Fe/H ] = -1.46 \pm 0.09 dex .
The absolute magnitudes M _ { V } 
and M _ { K } of RR Lyrae stars are linear functions of metallicity .
In the V band , our data agree with the Olech et al .
( 2003 ) relation , in the K band the slope is flatter .
The average apparent V luminosity of 70 RR Lyrae stars is < V > = 19.45 \pm 0.04 
and the average K luminosity of 37 RR Lyrae stars is < K > = 18.20 \pm 0.06 .
There is no obvious relation between apparent V magnitude and LogP , while the RR Lyrae K band magnitudes show a well defined linear trend with LogP .
Using the Bono et al .
( 2001 ) and Bono et al .
( 2003 ) theoretical Near-Infrared Period-Luminosity-Metallicity relations we calculate the LMC distance modulus \mu _ { 0 } = 18.48 \pm 0.08 .

Galaxies : individual ( LMC ) – Galaxies : Formation – Stars : RR Lyrae