Section
4
Using
Matrix
Operations
Matrix algebra
is a
powerful
tool.
It
allows
you to
more easily
formulate
and
solve many complicated problems, simplifying
otherwise
intricate
computations.
In
this
section
you
will
find
information
about
how the
HP-15C
performs certain matrix
operations
and
about using matrix operations
in
your applications.
Several results
from
numerical linear algebra theory
are
summarized
in
this
section. This material
is not
meant
to be
self-
contained.
You may
want
to
consult
a
reference
for
more complete
presentations.*
Understanding
the LU
Decomposition
The
HP-15C
can
solve systems
of
linear equations, invert matrices,
and
calculate determinants.
In
performing these calculations,
the
HP-15C
transforms
a
square matrix into
a
computationally
convenient
form
called
the L U
decomposition
of the
matrix.
The L U
decomposition procedure factors
a
square matrix
A
into
the
matrix product
LU.
L is a
lower-triangular
matrixt
with
1's
on
its
diagonal
and
with subdiagonal elements (those
below
the
diagonal) between
—1
and +1,
inclusive.
U is an
upper-triangular
matrix.!
For
example:
A
=
2
3
1 1
1 0
.5
1
2
3
0
-.5
= LU.
*
Two
such references
are
Atkinson, Kendall
E., An
Introduction
to
Numerical
Analysis,
Wiley,
1978.
Kahan,
W.
"Numerical Linear Algebra," Canadian Mathematical
Bulletin,
Volume
9,
1966,
pp.
756-801.
fA
lower-triangular matrix
has O's for all
elements above
its
diagonal.
An
upper-
triangular matrix
has
O's
for all
elements
below
its
diagonal.
96
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