April 2008
Intermediate
832 pages
26h 2m
English
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Problems and Computer Projects
PROBLEMS
Problem VIM (Rank of a matrix) Consider any N × M matrix H. Show that its row rank is equal to its column rank. That is, show that the number of independent columns is always equal to the number of independent rows (for any N and M), and hence, we can simply talk about the rank of a matrix.
Problem VII.2 (Frobenius norm of a matrix) Given an N × M matrix A of rank r, let 
denote its singular value decomposition (cf. Sec. B.6). Show that
Problem VII.3 (Projecting onto the orthogonal complement space) Consider an N × M full-rank matrix H with N ≥ M, and two column vectors y and z of dimensions N × 1 each. Let 
and 
. Are the residual vectors 
and 
collinear in general? If your answer is positive, justify it. If the answer is negative, can you give conditions ...
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