I read an article talking about MUltiple SIgnal Classification (MUSIC) algorithm at:
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?
We can form the projection onto the noise subspace; this
projection is given explicitly by
Pnoise=SIGMA vj v* (1)
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>