HP 15c - Manual (Page 119)

Section 4: Using Matrix Operations 119
) rows 1 (
), row 1 (
rows) (
ˆ
 











p n
p
q
0 0
0
g U
V
and Û is an upper-triangular matrix. If this factorization results from including n rows r
m
=
(x
m1
, x
m2
, …, x
mp
, y
m
) for m = 1, 2, ... , n in [X y], consider how to advance to n + 1 rows
by appending row r
n+1
to[X y]:



















 
1 1
1 0
0
n
T
n
r
V Q
r
y X
.
The zero rows of V are discarded.
Multiply the (p + 2) × (p + 1) matrix
) 1 (
) 1 (
) (
ˆ
1
row
row
rows p
q
n












r
0
g U
A
by a product of elementary orthogonal matrices, each differing from the identity matrix I
p+2
In only two rows and two columns. For k = 1, 2, ... , p + 1 in turn, the k th orthogonal matrix
acts on the k th and last rows to delete the k th element of the last row to alter subsequent
elements in the last row. The k th orthogonal matrix has the form



































C s
s c
1
0
1
1
0
1





where c = cos(θ), s = sin(θ), and θ = tan
-1
(a
p+2,k
/ a
kk
). After p + 1 such factors have been
applied to matrix A, it will look like