We've had this pair of cardinals around our house for a couple of weeks now. The female has been flying into our window repeatedly, so I got window chalk and wrote on it, "Not the sky! No fly zone!" That slowed her down some. Today I come home and she is going back and forth between two garden mirrors trying to attack her reflection as her mate looks on. I saw him shaking his head once. I took a short video. UGH! The link won't show you the video, but it will show you a shot of her in mid air.
Here is a link that might be useful: Stupid cardinal