Matematik
gram schmidt
16. april 2008 af
stræber-pigen (Slettet)
Let A be an m n matrix of rank n and let b € R^m.
If Q and R are the matrices derived from applying the Gram-Schmidt process to the column vectors of A and
p = c_1 * q_1 + ... + c_n * q_n
is the projection of b onto R(A), then show that:
a) c = Q^T b
b) p = QQ^T *b
c) QQ^t = A(A^T * A ) ^-1 * A^T
If Q and R are the matrices derived from applying the Gram-Schmidt process to the column vectors of A and
p = c_1 * q_1 + ... + c_n * q_n
is the projection of b onto R(A), then show that:
a) c = Q^T b
b) p = QQ^T *b
c) QQ^t = A(A^T * A ) ^-1 * A^T
Svar #1
16. april 2008 af stræber-pigen (Slettet)
Er der nogen der kan løse den?
A^T betyder den transponerende matrix.
R(A) er søjlerummet af A.
A^T betyder den transponerende matrix.
R(A) er søjlerummet af A.
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