Partially isometric matrices
John Z. Hearon · Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics · 1967
Th e complex, not necessaril y square matrix A is called a partial isom etry if the vectors x a nd A x ha ve the sam e Euclidean norm whe never x is in the orthogo nal co mple me nt of the null s pace of A .The main result s of th e paper give necessary and sufficient conditions for a matrix to be a partial isometry, for a partial iso metry to be normal and for the produ ct of two partial isometri es to be a partial isometry.A factorization for an arbitrary ma trix involving partial isometries is giv e n.The conce pt of a ge ne ralized inverse is used in establishing the primary results.