Unitary rectangular matrix
- From: "spasmous" <spasmous@xxxxxxxxx>
- Date: 29 Dec 2005 12:55:37 -0800
A situation I'm wondering about is where there's a signal (vector) f of
length n which is Fourier transformed by multiplication with the
unitary nxn matrix A, ie. F = A * f. The matrix A is unitary, A' * A =
I.
Now a new signal datum becomes available, say f[0] is repeated - I can
either average this with the old f[0] and keep the same matrix or
insert it on the end of f and add another row to A, which becomes
(n+1)xn. Clearly the new row is identical to row 0. Doing this for a
simple test case
>> A=[1 1;1 -1]/sqrt(2);
>> A'*A
ans =
1.0000 0
0 1.0000
All is fine. Now adding the repeated row, the above no longer holds.
This leads to my question: is there an mxn matrix A for which A' * A =
I? Or, at least, for which || I - A' * A || is minimum?
.
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