What kind of spider is this
You can relax; the spider is not a brown recluse, Loxosceles reclusa. It’s a bit difficult to identify which spider is in your image because it appears to have been whacked, thereby distorting its shape. The marks on the top of the abdomen remind me of a jumping spider, but that’s only a wild guess.
The good news is that the brown recluse is not in the LA, CA, area. Here’s a nice image of the brown recluse which, as you can see, is far different than the spider in your image: http://spiders.ucr.edu/brs.html. (Also notice the various informational links at the left of that page.) When you click the link in the caption under the photo, you’ll see a map showing the normal habitat the south-central US: http://spiders.ucr.edu/images/colorloxmap.gif.