Texas Instruments TI-89 Titanium User Manual page 835

QR
MATH/Matrix menu
matrix qMatName
QR ,
Calculates the Householder QR factorization of a
real or complex
matrices are stored to the specified
Q matrix is unitary. The R matrix is upper triangular.
Optionally, any matrix element is treated as zero if
its absolute value is less than
used only if the matrix has floating-point entries and
does not contain any symbolic variables that have
not been assigned a value. Otherwise,
• If you use ¥ ¸ or set the mode to
Exact/Approx=APPROXIMATE
are done using floating-point arithmetic.
• If
is omitted or not used, the default tolerance
tol
is calculated as:
ë 14 ù max(dim(
5
E
The QR factorization is computed numerically using
Householder transformations. The symbolic solution
is computed using Gram-Schmidt. The columns in
qMatName
span the space defined by
QuadReg
MATH/Statistics/Regressions menu
list1 list2
QuadReg ,
Calculates the quadratic polynomial regression and
updates the system statistics variables.
All the lists must have equal dimensions except for
.
list5
represents xlist.
list1
represents ylist.
list2
represents frequency.
list3
represents category codes.
list4
represents category include list.
list5
832
rMatName [ tol ]
, ,
. The resulting Q and R
matrix
MatNames
. This tolerance is
tol
, computations
matrix )) ù rowNorm(
are the orthonormal basis vectors that
.
matrix
[ ]
list3 list4 list5
, [ ] [, , ]
The floating-point number (9.) in
results to be calculated in floating-point form.
[1,2,3;4,5,6;7,8,9.]!m1 ¸
. The
QR m1,qm,rm ¸
is ignored.
tol
qm ¸
rm ¸
matrix
)
[m,n;o,p]!m1 ¸
QR m1,qm,rm ¸
qm ¸


m

m
rm ¸
In function graphing mode:
{0,1,2,3,4,5,6,7}! L1 ¸
{4,3,1,1,2,2,3,3}! L2 ¸
QuadReg L1,L2 ¸
ShowStat ¸
Appendix A: Functions and Instructions
causes
m1

1 2

4 5

7 8

.123... .904... .408...

ë.816...
.492... .301...

ë.301...
.861... .408...

8.124... 9.601... 11.078...

0. .904... 1.809...

0. 0. 0.


ë sign(møpì nøo)øo
m
+ o m + o
2 2 2 2
o møsign(møpì nøo)
+ o m + o
2 2 2 2

møn+oøp
m + o
2 2

m
ø
|

m pì n
0
m + o
2
{1 2 3
{4 3 1

3

6

9.
Done







m n

o p
Done





+ o
2 2
ø
|

o
2
... }
... }
Done