Hi,

I read an article talking about MUltiple SIgnal Classification (MUSIC) algorithm at:

http://www.physics.sfsu.edu/~dcuneo/radar-mount/music.pdf

When I read the following on page 2 (I change above bar and T to a conjugate * for difficulties in writing above bar here), I cannot understand the last line. The project matrix is still a (transformation) matrix, but it said inner product. I remember that the inner product is a scalar. I also cannot understand "that maps a vector f". Where is mapping in the noise subspace topic?

Thanks,


.............
We can form the projection onto the noise subspace; this
projection is given explicitly by

                
Pnoise=SIGMA vj v*            (1)
        j>M   

where the superscript 0 denotes transpose, the bar denotes complex conjugate,
and v* is the linear functional that maps a vector f to the inner product <vj, f>