148 Section 12: Calculating with Matrices
operate on the matrices whose descriptors are placed in the X-register and
(for some operations) the Y-register.
Two matrix operations – calculating a determinant and solving the matrix
equation
AX
=
B
– involve calculating an
LU
decomposition (also known
as an
LU factorization
) of the matrix specified in the X-register.
*
A matrix
that is an
LU
decomposition is signified by two dashes following the matrix
name in the display of its descriptor. (Refer to page 160 for using a matrix
in
LU
form.)
The Result Matrix
For many operations discussed in this section, you need to define the matrix
in which the result of the operation should be stored. This matrix is called
the
result matrix
.
Other matrix operations do
not
use or affect the result matrix. (This is noted
in the descriptions of these operations.) Such an operation either replaces
the original matrix with the result of the operation (if the result is a matrix,
such as a transpose) or returns a number to the X-register (if the result is a
number, such as a row norm).
Before you perform an operation that uses the result matrix, you must
designate the result matrix. Do this by pressing
´
<
followed by
the letter key specifying the matrix, (If the descriptor of the intended result
matrix is already in the X-register, you can press
O<
instead.)
The designated matrix remains the result matrix until another is designated.
†
To display the descriptor of the result matrix, press
l
<
.
When you perform an operation that affects the result matrix, the matrix is
automatically redimensioned to the proper size. If this redimensioning
would require more additional elements than there are available in matrix
memory (a
maximum
of 64 for all five matrices), then the operation can't be
performed. This restriction can often be overcome by designating the result
matrix to be one of the matrices being operated on. (However, there are
certain operations for which the result matrix can
not
be the same one as
either of the matrices being operated on – this is noted in the description of
these operations.)
*
The
LU
decomposition of a matrix
A
is another matrix in which is encoded a lower-triangular matrix
,
L
,
and an upper-triangular matrix,
U
, whose product
LU
equals matrix
A
(possibly with same rows
interchanged). The
HP-15C Advanced Functions Handbook
discusses
LU
decomposition in detail.
†
Matrix
A
is
automatically
designated as the result matrix whenever Continuous Memory is
reset.
Summary of Contents for HP-15C
Page 1: ...HP 15C Owner s Handbook HP Part Number 00015 90001 Edition 2 4 Sep 2011 ...
Page 17: ...Part l HP 15C Fundamentals ...
Page 64: ......
Page 65: ...Part ll HP 15C Programming ...
Page 118: ...118 ...
