QR Decomposition

We will begin with a rectangular matrix A, and we will be able to solve this system by decomposing A into an orthogonal matrix Q and an upper triangular matrix R (using QR decomposition), i.e A = QR.

We will first convert the columns of the matrix A into Vectors. Then, for each vector ak, we will calculate the vectors uk and ek given by

uk = [Sigma]i = 1 to k-1projej ak
and
ek = uk / ||uk||
Then

Q = [e1, ..., en] and

R =
<e1, a1><e1, a2><e1, a3>
0<e2, a2><e2, a3>
00<e3, a3>

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